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Other Refs. include especia physicists and A field. by us, the written of career. tributes all entering and and for life people resource his valuable young a in to be faced can he they [ difficulties such poig recollections the and own refreshingly about are Polchinski’s honest They study fascinating. to truly are reader which the urge We gis hs ds o aepoon n lasting and profound made Joe odds, these Against hsisgtldt rmtcpors nsvrldeep several on progress dramatic to led insight This strongly to applied be not could theory string But Be- physics. theoretical in watershed a mark D-branes ∗ e eouinzdsrn hoyadled and theory string revolutionized nes rtr n nacmlse athlete. accomplished an and writer, udcalne o a epydevoted deeply was Joe challenge. ound ,adt omlg,adesn the addressing cosmology, to and p, t.Hsrcn,icsv reformulation incisive recent, His ity. tclpyiit fteps 0years, 50 past the of physicists etical 1 tlcnrbtost quantum to contributions ntal o’ otsgicn ok nld the include works significant most Joe’s si,T 81,USA 78712, TX ustin, USA , nantly lly 1], es e s 2 many of these developments. His D- paper [6] and III. EARLY CAREER AND FIRST IMPORTANT his nearly simultaneous work with Witten [7] form cor- RESULTS nerstones of the “second superstring revolution,” which unified what were then five distinct versions of string the- Having published zero papers as a graduate student ory. was not the academic death sentence it might be today. We see the impact of Polchinski’s discovery in the qual- Joe went on to SLAC for his first postdoc. There he ity of the work it elicited in other leading physicists. Stro- worked with , who would become an minger and Vafa [8] succeeded in describing certain black important lifelong influence. holes microscopically as stacks of D-branes. They were Joe and Lenny studied several aspects of supersymme- able, for the first time, to compute the en- try. During the early 1980’s several groups had realized tropy statistically, matching the thermodynamic formula that the special quantum behaviour of supersymmetric of Bekenstein and Hawking which is considered one of field theories could play an important role in physics be- the greatest successes of . Within a year, yond the Standard Model. The Lagrangian of the sim- Banks, Fischler, Shenker and Susskind [9] formulated plest supersymmetric gauge theories N = ∞ consists of , using a large number of D0-branes to pro- two terms, denoted F and D terms. F-terms were al- vide the first concrete proposal for a nonperturbative de- ready known not to be affected by quantum corrections. scription of string theory (often referred to as M-theory). In their first article, together with , Pe- In 1997, Maldacena formulated his celebrated Anti-de ter Nilles and Stuart Raby [17], Joe and Lenny proved Sitter/ conjecture [10], provid- that the D-terms were also not renormalized by quantum ing a complete, nonperturbative definition of a quantum corrections as long as the sum of all the charges of the theory of gravity in a large class of spacetimes. The in- matter fields is zero (a condition that was later identified sight that we might live on a D-brane [11–13] opened vast as the absence of gravitational anomalies). new directions in particle phenomenology. And finally, Second, Joe and Susskind [18] were able to prove that D-branes and their associated fluxes underlie the string the energy scale of breaking could be landscape [14–16], as we discuss below in the context of much higher than the scale that determines the difference the problem. in mass between and (which to address D-branes were not mere catalysts of these develop- the hierarchy problem was expected to be close to the ments. Rather, they play a central role in the new fields TeV scale). They presented arguments and detailed cal- that formed in their wake. They have become a ubiqui- culations to show the stability of scales and the natural tous tool, nearly as familiar to today’s graduate students presence of a “hidden sector” in supersymmetric exten- as quantum fields. Their applications range far beyond sions of the Standard Model. In the Standard Model, the particle physics and , to problems such symmetry breaking sector (the Higgs) couples directly to as superconductivity and the quark-gluon plasma. the matter sector. But in supersymmetric theories, the sector that breaks supersymmetry does not have to cou- ple directly to the observable sector, and the source of supersymmetry breaking can be at much higher energies. II. EARLY LIFE These ideas have been behind the subsequent efforts to- wards gravity mediation in and string the- Joseph Gerard Polchinski Jr. was born in White Plains, ory constructions. N.Y., on May 16, 1954, to Joseph and Joan Polchin- For his second postdoc at Harvard, Joe started to ski (née Thornton). He grew up there and in Tucson, collaborate with Mark Wise and Luis Alvarez-Gaumé Arizona, developing an early fascination with math and [19]. They managed to implement electroweak symme- physics. He went to Caltech, where his interests included try breaking in a supersymmetric version of the Stan- devising pranks with his friend, the physicist Bill Zajc, dard Model by using the renormalization group running, as well as taking classes with Richard Feynman and Kip in the sense that a negative quadratic term for the Higgs Thorne [1]. field needed for electroweak symmetry breaking is natu- For graduate school, Joe picked Berkeley, partly out rally induced by having a very heavy top mass running in of his love of California, partly because of a Hertz fel- the loops. This result (obtained independently by Luis lowship. He worked with on quark Ibáñez and Graham Ross [20] ) gave a strong argument confinement and—unsurprisingly, given the difficulty of in favour of supersymmetric extensions of the Standard the problem—published nothing at all in his entire grad- Model. This was reinforced by the discovery in the 1990s uate career. In his “Memories,” Joe blames his own “lack of the top quark with a very heavy mass, precisely as of common sense and of any collaborative instinct.” needed for this radiative electroweak symmetry breaking. We deliberately keep this section short, in the hope In an important single-author paper while at Harvard that it will provoke readers to read Joe’s “Memories” [1]. [21] Joe was able to extend the Wilsonian approach to They are a fascinating, concise, and beautifully written renormalization to arbitrary cut-offs and to derive a func- account of his life and work. Below we offer our perspec- tional equation for the renormalized action. In this re- tive on Polchinski the physicist. gard, he pioneered the development of the “exact renor- 3 malization group” formalism, in which a single compli- corresponding string amplitude that helps to identify D- cated equation embodies all of the usual renormalization branes as solitonic non-perturbative objects of different group equations to all orders in perturbation theory. He dimensionalities carrying both tension and charge. He proved that under broad conditions, any theory formu- established the generalized Dirac quantization condition, lated with an ultraviolet cut-off will flow to a renormal- similar to monopoles. D-branes are charged not under izable theory as the cut-off is decreased. electromagnetic field but under more general antisym- Joe’s arrival at the University of Texas, Austin, essen- metric tensor fields appearing in the spectrum of string tially coincided with the start of the first string theory theories. revolution. Joe immediately started playing a leading role in the Weinberg theory group. He wrote a beautiful paper on the one-loop amplitude for the closed bosonic V. EXPLAINING THE SMALLNESS OF THE string in the path integral Polyakov formalism [22]. This COSMOLOGICAL CONSTANT explicit calculation of the vacuum amplitude emphasized the crucial role of modular invariance, the difference with In 1999, Polchinski turned his attention to the prob- the field theory spectrum, and the relation to the finite lem of the cosmological constant (CC). A nonzero CC was temperature partition function. It had an enormous im- first introduced by Einstein in a futile and misguided at- pact in the string community, and it led to many further tempt to make his general theory of relativity compatible developments both in bosonic and supersymmetric string with a presumed static universe. In Einstein’s equation, theory. the CC is mathematically equivalent to the energy den- sity of the vacuum, which was later recognized to be an inevitable feature of quantum field theory.3 Contribu- IV. D-BRANES tions to the density from Standard Model fields are at least 60 orders of magnitude larger than the value first observed in 1998 [29, 30] (and long-known up- In this section, we will focus on the lead-up to Polchin- per bounds). How come they cancel to such exquisite ski’s discovery of D-branes, as we have already discussed precision? This is the cosmological constant problem: its impact and significance in the introduction. why is the vacuum energy so tiny?4 In 1986, with his students Jim Hughes and Jun One of the present authors (SW) had recognized in Liu [23], he found the effective action of supersymmetric the 1980s that the unnatural smallness of the CC may branes, in an attempt to understand partial supersym- be a selection effect [35]. A very small CC is needed for N = 2 → N = 1 metry breaking ( ) in supersymmetric large structures to form in the universe. Perhaps there field theories. This article directly led to the work of are many regions with different values of the CC, and Eric Bergshoeff, Ergin Sezgin and Paul Townsend [24] observers find themselves where structure is possible? If on the maximal 11-dimensional supermembrane, which so, the CC should not be much smaller than the present in turn triggered the early work on general p-branes [25]. matter density. This proposal would have been ruled In 1989, in a completely different project, Joe sought out by significantly tightened upper bounds on the CC. an improved understanding of T-duality, the string sym- But instead a positive value was observed in 1998—just metry relating large to small distances. With his stu- what would be expected if the CC was biased by observer dents Jin Dai and Robert Leigh, he discovered that T- selection, among many possible locations in the universe. duality for open strings exchanges Neumann and Dirich- Yet, it proved difficult to implement the idea of the CC let boundary conditions [26]. In the latter case the end- as a selection effect, at the concrete level of obtaining a points of the string had to be fixed at a lower-dimensional 2 theory with suitable vacuum structure and yet with dy- surface, which they denoted Dirichlet-brane or D-brane. namics consistent with the observed big bang cosmology. Due to the presence of gravity in string theory, these ob- jects are not rigid surfaces but must be dynamical. In 1992 Joe moved to Santa Barbara as one of the few faculty members of the Institute for 3 A more recent name for the CC (aside from “vacuum energy”) is (now KITP). Three years later he realised the crucial “dark energy.” This terminology encourages us to keep an open role that D-branes can play in the equivalence among mind: perhaps the acceleration of the expansion of the universe is driven by a time-dependent effect. However, such models are all different string theories, hints of which had begun to strictly more complicated than a pure CC. They fine-tune the emerge by then. In a short paper [6] he computed the CC but contain additional parameters that need to be tuned. In more than two decades since the first measurement of the CC, no observational evidence has emerged that would compel us to consider such complications. 4 For reviews of the CC problem, see Refs. [31–33]; the latter two 2 In this same article the concept and name of was references also summarize the Bousso-Polchinski proposal. For a introduced. It corresponds to simultaneous twists in target space nontechnical summary, see Ref. [34]. Joe offers his own account and the string , generalizing the standard concept of of the gestation and impact of this work in Sec. 9.6 of Ref. [1]: its . Related work was done by Augusto Sagnotti [27] and implications troubled him greatly, but “one must follow science Petr Hořava [28] independently. where it leads” (Sec. 10.7). 4

First, the required number of vacua (long-lived field con- one possible outcome of a chain of such transitions. figurations, each with different CC) would have to exceed 10123. How would a simple theory give rise to so many different versions of empty space? Secondly, if one sim- VI. MODULI STABILIZATION ply posits an effective potential with a huge number of minima, the theory runs into sharp conflict with obser- Stabilizing the size and shape of the extra dimensions vation: it predicts a universe with far too little matter has been a major challenge for higher dimensional the- and radiation. These problems, first articulated by Ab- ories since the original work of Kaluza and Klein in the bott and others in the 1980s, appeared severe and stood early 20th century. Among the most influential theoret- unsolved [36, 37]. ical articles of the first decade of this century is “Hier- In Polchinski’s work with one of the present authors archies from fluxes in string compatifications” by Gid- (RB) [14], a key insight was to think of D-branes as build- dings, Kachru, and Polchinski (GKP) [15]. This article ing blocks of empty space. String theory has 9 spatial established how fluxes of antisymmetric tensor fields can dimensions, so our observation of only 3 requires that stabilize many of the different moduli (shape and size of 6 are “compactified” and too small to observe. There the extra dimensions), as anticipated in Ref. [14]. GKP were many ways one could envisage doing this, but all left only a class of moduli known as Kähler moduli un- known approaches would lead to new long-range fields or fixed, but with the interesting outcome that they break to a negative value of the CC, neither of which are ob- supersymmetry while still keeping vanishing cosmologi- served. Polchinski noticed that the presence of D-branes cal constant at tree-level, a property known as no-scale and their associated fluxes in the extra dimensions would supergravity. have profound implications. They would make it possible This work triggered the subsequent work of Kachru, to avoid unwanted light fields (this was corroborated by Kallosh, Linde and Trivedi [16] (KKLT) that added non- later work of Kachru et al. as we will see next), and to perturbative effects and antibranes to also fix the Kähler obtain a vacuum such as ours in string theory. moduli and uplift the minimum to de Sitter space. Moreover, D-branes and fluxes greatly increase the The GKP construction is very explicit, illustrating how number of possible ways to make what a low-energy ob- three-form fluxes fix the and complex structure server would perceive as empty space. Simple combina- moduli (sizes of three-cycles) with a concrete description torics yields an enormous number of vacua and hence, a both from 10 dimensions and from the four dimensional dense spectrum of the CC. This solved the first challenge effective actions. This construction underlies the string in implementing Weinberg’s approach. theory landscape [14], in the sense that the source of the Because fluxes can wrap different topological cycles, large number of metastable solutions are precisely the one obtains a high-dimensional effective potential (a fluxes in the GKP part of the full GKP and KKLT con- “landscape”). Neighboring vacua can have enormously structions. The fluxes are integers due to a Dirac quanti- different vacuum energy, yet all the vacua can be popu- zation condition but several integers can take a range of lated by the cosmological dynamics. When one vacuum values, leading to an enormous number of possible com- decays, matter and radiation can be produced in the re- binations. These properties were anticipated by Bousso gion containing the new vacuum. This addressed the and Polchinski in their approach to the cosmological con- second challenge, allowing for a hot big bang. stant problem. The GKP and KKLT constructions lend Whether a large landscape of vacua is the correct solu- substantial support to the BP proposal, by providing an tion to the CC problem is not known. The vacuum struc- explicit string theory realization of the scenario. ture of Nature, like any other scientific question, must be Independently of the cosmological constant problem, settled by observation. We lack the technology to probe moduli stabilization removed a major stumbling block for our vacuum at the required energies, and our theoret- string theory to make contact with low-energy physics. ical control is not yet strong enough to devise decisive (Massless moduli fields would mediate long range interac- indirect tests. tions, contrary to observations.) Moreover, the GKP flux But it is significant that after more than 40 years of se- compactifications naturally induce warping in the extra rious attempts at the CC problem, Polchinski’s insights dimensions which explicitly realize the popular Randall- underly the only known viable approach. If the land- Sundrum scenario in string theory. In this sense the scape proves correct, it is a revolution. The particles warping introduces a natural way to create hierarchies and forces we observe would not be unique. This chal- that may connect the Planck scale to smaller scales such lenges naturalness as the dominant paradigm of particle as the TeV scale governing the Standard Model. physics: selection effects, rather than symmetries, may The GKP and KKLT constructions influenced thou- explain not only the CC but also other parameters such sands of articles addressing concrete phenomenologi- as masses and couplings. (Indeed, a natural origin of the cal and cosmological questions of string compactifica- scale of the weak interaction is already in tension with tions. In one proposal, collisions of Polchinski’s D- and may eventually be ruled out by present and future branes and anti-branes may give rise to cosmological in- accelerators.) In cosmology, the big bang would corre- flation [38, 39]. The annihilation process can also pro- spond to a phase transition, and the visible universe to duce lower dimensional branes such as relic cosmic strings 5 that could give rise to observational signatures [39, 40]. space everywhere else. This is a straightforward conse- Joe’s deep physical intuition immediately entered in ac- quence of Einstein’s general theory of relativity. If this tion and explored its consequences together with Ed- assumption were wrong, Einstein’s theory would seem to mund Copeland and Rob Myers [41]. Potential observa- break down completely. It would fail in a regime where it tion of cosmic strings is one of the very few opportunities was expected to be arbitrarily accurate, namely far from to test string theoretical ideas at very high energies. the quantum domain, when the curvatures of space and Moduli stabilization and its potential physical impli- time are small. cations is still a very active research area. In one of his In the early 1990s, Gerard ’t Hooft, Leonard Susskind, very last projects Joe managed to solve a challenge re- John Preskill and others came up with an unorthodox garding an obstruction to consistently have anti-branes attempt to thread the needle, hoping to save quantum in the presence of fluxes that give rise to de Sitter space mechanics without breaking . This idea in KKLT [42]. This settled a long debate in the subject. became known as black hole complementarity [47], as it assigned two “complementary” descriptions to the black hole. Viewed from the outside, it would behave like any VII. BLACK HOLES, INFORMATION, AND other object, with some actual structure at the hori- FIREWALLS zon that would preserve information about the quantum state, in harmony with the quantum mechanical evo- The history of the black hole information paradox is lution tested by this observer. Yet, an observer freely full of unexpected turns and surprises. Jacob Beken- falling across the horizon would experience nothing spe- stein’s 1972 conjecture [43] that black holes carry entropy cial, just empty space, as dictated for that observer by was at first rejected by [44]. Ironi- general relativity. cally, Hawking’s objection was that Bekenstein’s entropy Naively these two descriptions conflict. But comple- would imply a nonzero temperature (by the First Law), mentarity cleverly exploited some undeniable facts about and hence would require black holes to radiate thermally. black holes. By definition, an observer inside the black This seemed absurd, because classical black holes cannot hole cannot send a signal to the exterior, nor could she emit anything. But in an unrelated calculation, Hawk- return to the outside to check whether or not informa- ing soon found that black holes do radiate, by a quantum tion was lost. Perhaps more surprisingly, one can also effect [45]. When no infalling matter compensates, this check that an observer on the outside cannot send a sig- implies that a black hole eventually loses all of its mass nal to a friend (say, that the information came out), if and disappears. It will then have returned the corre- the latter entered a black hole too long ago. These ob- sponding amount of energy to the exterior in the form of structions seemed to conspire against any possibility of a cloud. verifying the apparent differences in their description of Hawking was able to show, moreover, that the quan- the black hole. It thus appeared that no contradictions tum state of the radiation would be mixed (roughly, ther- between general relativity and quantum mechanics would mal) [46]. Thus the final state would be essentially be encountered in any conceivable experiment involving unique, in that it would depend only on the mass and large black holes, so long as the experiment itself did not angular momentum of the matter that made the black violate known laws of physics. hole. It would not otherwise depend on its initial quan- Though some physicists (notably, Samir Mathur) were tum state. vocally skeptical about its viability, complementarity is This was a shocking claim. It meant that the unitarity where things stood for nearly 20 years. But in 2012, of quantum mechanics would break down in the presence Polchinski (working with A. Almheiri, D. Marolf, and of a black hole. Normally, one can use the Schrödinger J. Sully) found a sharp contradiction in the frame- equation to evolve a quantum state forward or backward work [48]. Complementarity was not enough to resolve in time. The state at a different time is computed by the black hole information paradox. The AMPS collabo- the action of a unitary operator that depends on the dy- ration accomplished this by taking advantage of some of namics. This map is one-to-one, allowing for perfect pre- the counterintuitive properties of quantum information. dictability. For large systems, this remains true at least They showed that the joint assumptions of unitarity and in principle, if not in practice due to limited control. But empty space at the horizon would allow for the construc- for black holes, Hawking found that unitarity would be tion of an impossible quantum state in the laboratory of false even as a matter of principle. Any pure state result- an observer entering the black hole. One of these assump- ing in a black hole of a given mass and angular momen- tions (or else the validity of effective field theory outside tum would be mapped to the same mixed state, that is, the black hole) would have to be abandoned. to a classical probability distribution over pure states. If the AMPS paper had appeared 30 years earlier, it Hawking’s claim disturbed many physicists, as it chal- might have convinced many physicists of Hawking’s claim lenged a core principle of quantum mechanics. But no that information is lost. Since Hawking’s original work, error was found in his calculation, and his assumptions however, the theoretical prior had shifted significantly to- seemed innocuous: mainly, that the horizon of a large wards unitarity. The AdS/CFT correspondence defined black hole, when no matter is falling in, is just like empty a compelling quantum gravity theory in a setting where 6 the formation and evaporation of black holes can occur, is becoming more relevant today, as the condensed matter and it simply did not allow for information to be lost. and high energy communities are finding closer common With no wiggle room for a compromise like comple- research interests. He has also several articles on the mentarity, AMPS argued that the most conservative con- applications to condensed matter of the AdS/CFT cor- clusion was a complete breakdown of general relativity at respondence, and much earlier a pure condensed matter the horizon. But what replaces empty space? With min- article with Fisher and Kane [50] on the quantum Hall imal assumptions, AMPS showed that all quantum fields effect. would be excited at arbitrarily small distance scales near “Polchinski’s paradox” refers to an obstacle he formu- the horizon, and hence at very high energies. Instead of lated to a proposal by and collaborators: the empty space, the boundary of a black hole would be a possibility of using to travel in time. Joe’s “firewall.” idea was to throw a billiard ball through a in Firewalls came as an absolute shock to many in the such a way that after coming out in the past it hits it- quantum gravity community. It took a mind like Joe’s self, preventing itself from entering the wormhole. This to cut through the preconceptions and return us to the is better known in the popular science literature [51]. stark choice between information loss and a total break- Polchinski made an important contribution to the down of Einstein’s theory. Something big has to give, so foundations of quantum mechanics. He successfully tor- the firewall crisis is likely to contribute to a major leap pedoed a possible generalization of quantum mechan- in our understanding of Nature. An army of physicists is ics invented by one of us (SW), by showing that it sharpening its tools, hoping to determine how to get rid would allow instantaneous communication at a distance, of firewalls, or else to understand how they would form and even communication between different histories in and persist. We are developing powerful new methods a many-histories interpretation of quantum mechanics. and applying ever more sophisticated techniques from This work has set an important constraint on any fu- quantum information theory to the study of spacetime ture attempt to go beyond the usual version of quantum and gravity. mechanics.

VIII. THE BROAD THEORIST IX. JOE’S LEGACY

Even though most of Joe’s efforts concentrated in the Joe has left a vast legacy in many respects. As a family development of string theory, he was a theoretical physi- man, he is dearly missed by his wife Dorothy and his sons cist in the broadest sense. Many theorists are at home Steve and Daniel. As a great scientist with the deepest only in a very narrow range of highly mathematical top- mind, tremendous physical intuition, impressive calcula- ics. Polchinksi was different. He did work of real impor- tional tools, a wide knowledge and a deep understanding tance in a remarkable variety of fields. of theoretical physics, he was admired and respected by With Fischler, Polchinski challenged what seemed to his colleagues. His students enjoyed his unusual gift for be a breakthrough by Sidney Coleman and Stephen combining friendliness and brilliance. Hawking in understanding the cosmological constant. He dedicated much of his research efforts to string the- They had claimed that quantum fluctuations produce a ory. Indeed, he did not shy from publicly defending and probability distribution for the vacuum energy that is promoting work in this field, so in a way he represented sharply peaked at value zero, but Fischler and Polchin- “the voice of string theory.” ski showed that the approximations used by Coleman and But as we mentioned at the outset, Joe always thought Hawking cannot be trusted. Furthermore, together with of himself as a “theoretical physicist first, string theorist Fischler and Morgan [49], he developed a general formal- second.” (This is a literal quote, to one of us, RB.) This ism to study vacuum transitions through bubble nucle- attitude is reflected in the breadth and richness of his ation in semiclassical gravity, generalising and putting on knowledge, and in his research achievements spanning firmer grounds previous work of Coleman and De Luccia cosmology, particle physics, black holes, and condensed as well as of the general ideas of Farhi, Guth and Guven matter physics. on the possibility of creating a universe in the laboratory. His lectures were masterpieces of clarity, elegance and Polchinski pioneered several applications of the renor- logical presentation, never exceeding the appropriate malization group to quantum field theory and, as men- number of words. His writing skills were unparalleled. tioned above, made fundamental contributions to the for- Besides his two major string theory textbooks [52], he mulation of the renormalization group. He also wrote a wrote beautiful reviews on many aspects of theoretical beautiful article on the effective field theory approach to physics (see for example[53–58]). They remain the stan- describe Fermi liquids, an elegant contribution to con- dard ways to introduce the corresponding field. His fa- densed matter physics inspired by general ideas of effec- mous “star” plot of all string theories being related to tive quantum field theories. Using his own words, Joe each other has been reproduced in many presentations as proved that BCS superconductivity was due to asymp- the standard way to explain the unity of string theories. totic freedom just as the confining of quarks. This article His introduction of terms such as D-branes, orientifolds, 7 discretuum, etc. are part of the daily vocabulary among In him, there was something of an oracle. thousands of theoretical physics worldwide. For all of us who had the privilege to know him, he has And to remember typical expressions that all of us left an indelible mark. He was open enough to listen to who met Joe will never forget: everybody independently of their status. He was patient enough to explain physics concepts to less expert col- Among my favourite memories as a scientist are leagues or students. He was kind enough to give respect moments when I taught Joe something he did not know; and dedicate time to everybody. he would be silent for a few seconds, nodding rapidly, Joe was a human being living life to its fullest. He loved with an intent look -his eyes narrow and his mouth and obsessed over physical exercise (including estimating slightly open- as he absorbed the point. in real time the number of calories he was consuming in every meal and decide how much extra exercise he would We may add to this his tendency to close his eyes while need to do to compensate). explaining some deep concept. One of his famous anec- Regarding his many qualities as a researcher, one of dotes was that he fell asleep during one of his own lectures his main collaborators, Matt Strassler recalls witnessing in ICTP in 1995 while doing this. Joe’s calculational skills and physic intuition [5]: Looking to the future, we can be confident that Joe’s imprint will be present in any new discovery about the Each calculation was unique, a little gem, involving fundamental understanding of Nature. D-branes could a distinctive investigation of exotically-shaped D-branes be the basic building blocks of matter; they appear to sitting in a curved space. It was breathtaking to wit- be the underlying degrees of freedom inside a black hole. ness the speed with which Joe worked, the breadth and They can also be whole universes, and they are the build- depth of his mathematical talent, and his unmatched ing blocks of the that we may inhabit. understanding of these branes.... Somehow his mind was As Joe once quipped, he discovered both the smallest working in places that language does not go, in ways and the largest things. What better legacy could one that none of us outside his brain will ever understand. hope for?

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