DOCSLIB.ORG

Dynamical Spacetimes from Numerical Hydrodynamics

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Dynamical Spacetimes from Numerical Hydrodynamics MIT-CTP-4607 Dynamical Spacetimes from Numerical Hydrodynamics Allan Adams,1 Nathan Benjamin,1, 2 Arvin Moghaddam,1, 3 and Wojciech Musial1, 3 1Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139 2Stanford Institute for Theoretical Physics, Stanford University, Stanford, CA 94305 3Center for Theoretical Physics, University of California, Berkeley, Berkeley, CA 94720 We numerically construct dynamical asymptotically-AdS4 metrics by evaluating the fluid/gravity metric on numerical solutions of dissipative hydrodynamics in (2+1) dimensions. The resulting numerical metrics satisfy Einstein's equations in (3+1) dimensions to high accuracy. Holography provides a precise relationship between Review of Fluid/Gravity black holes in AdSd+1 and QFTs in d-dimensions at fi- nite density and temperature. When the QFT state lies We begin by recalling the essential features of the in a hydrodynamic regime (i.e. when d-dimensional gra- fluid/gravity correspondence for a (2+1) fluid as given dients are sufficiently small that the stress-tensor may in [1{4]. At equilibrium, a fluid moving with constant 3- µ be expanded as a power-series in derivatives), the dual velocity u at temperature T is dual to an asymptotically spacetime metric may also be so expanded, leading to an AdS4 black brane described by the metric [10] analytic “fluid/gravity" map between solutions of hydro- ds2 = −2u dxµdr−r2f(br) u u dxµdxν +r2P dxµdxν ; dynamics in d dimensions and dynamical asymptotically- µ µ ν µν AdSd+1 solutions of the Einstein equations. 3 where b = 4πT is the rescaled inverse temperature, This suggests a simple strategy for constructing nu- P µν =ηµν +uµuν projects onto directions transverse to merical solutions of the Einstein equations in asymptot- µ 1 u , and f(ρ) = 1 − ρ3 is the emblackening factor. It is ically AdSd+1 spacetimes: rather than solve the (d+1)- readily checked that this metric solves the Einstein equa- dimensional Einstein equations numerically, we may nu- tions so long as uµ and T are constant. merically solve d-dimensional hydrodynamics and use the If uµ(x) and T (x) vary in space and time, it follows fluid/gravity map to analytically construct the corre- that this metric is again a solution of the Einstein equa- sponding metric. So long as the fluid flow lies sufficiently tions when expanded to leading (trivial) order in gra- deep in the hydro regime, the hydro equations can be dients. When all gradients are small, it is possible to truncated at a desired order in the gradient expansion; systematically improve the metric order-by-order in gra- the resulting fluid/gravity metric is then an analytic so- dients to construct a solution of the (d+1)-dimensional lution of the Einstein equations up to errors of corre- Einstein equations provided that uµ(x) and T (x) solve sponding order. Na¨ıvely, this should be a much easier the equations of d-dimensional hydrodynamics. calculation, since one need only solve PDEs in 3d, rather Demonstrating this is simplified by working in a gauge than 4d. The main question in principle is whether the in which the nth-order corrections take the form, resulting algorithm is sufficiently robust to small depar- 2 (n) µ 2 µ ν tures from the true hydro solution and numerical errors ds(n) = −h (2uµdx dr + r Pµν dx dx ) to be useful. In practice, this will also serve as an inde- 2 + k(n)u u dxµdxν + j(n) u dxµdxν + α(n)dxµdxν : pendent check of the analytic results in the literature. µ ν ν r µ µν In this paper we construct numerical solutions to 2nd order dissipative relativistic hydrodynamics, evalu- Upon expanding to nth-order in gradients, the rr and ate the fluid/gravity metric on the resulting flows, and µν components of the Einstein equation reduce to linear arXiv:1411.2001v1 [hep-th] 7 Nov 2014 test the satisfaction of the Einstein equations on the equations for the functions h(n), k(n), j(n) and α(n), corresponding dynamical spacetimes. Implementing the 1 d d fluid/gravity map revealed minor typos in the literature r4 h(n)(r; x) = S(n)(r; uµ(x)) r4 dr dr h which we corrected by re-deriving the fluid/gravity ana- d 2 lytic map.[9] The resulting numerical metrics satisfy the − k(n)(r; x) + (1 − 4r3)h(n)(r; x) = S(n)(r; uµ(x)) Einstein equations with great precision. Concretely, we dr r k find that when the flow is hydrodynamic, the 0th order r d 1 d j(n)(r; x) = S(n)(r; uµ(x)) fluid/gravity metric provides good approximation of a so- 2 dr r2 dr ν jν lution to the Einstein equations for a wide range of fluid d 1 d flows within the hydro regime, and that the 1st and 2nd − r4f(r) α(n)(r; x) = S(n) (r; uµ(x)) ; dr 2 dr µν αµν order corrections improve the accuracy of this fluid met- ric appropriately, leading to accurate numerical metrics (n) where the \source" functions S (r; uµ(x)) may be ex- computed at low computational expense. ∗ plicitly computed order-by-order in the gradient expan- sion and depend only on n or fewer derivatives. These 2 equations are manifestly local in the fluid dimensions, x, Eq (3) of [1]. Since we work with a 2nd order stress ten- so solving them reduces to a series of numerically-simple sor, the resulting conservation equations are third order 1-dimensional integration problems. in time-derivatives of the fluid variables. To avoid spuri- (1) ous solutions and simplify our calculation, we treat the At first order, the sources take simple forms, Sh = 0, µν (1) (1) 1 (1) dissipative stress tensor Π as an independent dynami- S = −4rr·β, S = − @tβi, and Sα = 2rσij, where k ji r ij cal variable whose evolution is determined by the consti- σ = 1 r β + r β − 1 δ r·β, β is the fluid velocity ij 2 i j j i 2 ij i tutive relations a la Israel-Stewart. So long as we remain in the local rest frame at position x, β (x) = 0, and i, j i within the hydrodynamic regime, solutions of the result- label the spatial dimensions.[11] ing equations should relax toward solutions of the full Given these sources, the equations above can be inte- equations.[13] We use the satisfaction of the constitutive grated along the radial direction to give [12]: h(1) = 0, relations as a check on our numerical solutions. (1) 1 (1) (1) 3 (1) (1) 1 (1) k = − S , jµ = −r S , and αµν = Sα F (r), µν 4 k jµ r µν Upon fixing Landau gauge (uµΠ =0) and demanding where conformal invariance (Πµ =0), only 2 components of Πµν p µ −1 2r + 1 1 1 + r + r2 3π remain linearly independent. A convenient parameteri- F (r) = p Tan−1 p + log + ; zation for these two dissipative variables involves setting 3 3 2 r2 6 Π = (2 + u2 + u2)Π ; as presented in [1]. xy x y 2 At second order the sources are somewhat more cum- Πxx = 2(1 + ux) Σ + 2uxuy Π : bersome, so we refer the reader to [1] whose 2nd order sources we have analytically verified modulo minor typos All other components of Πµν may then be determined in (2) terms of regular functions of uµ times Π and Σ. in S and F2, which we find take the values, k The hydro equations then take the form M(u)_u = b(u), 1 1 + 4r3 where u is a vector of our five variables (ux, uy, T ,Σ S(2) = 2S + S − S + F (r) S ; k 3 2 5 2r3 6 2 7 and Π), while the 5 × 5 matrix M(u) and the 5-vector 2(1 + r)(1 − 4r3) −1 + 2r + 4r2 + 4r3 b(u) are non-linear functions of u and its spatial (but not F = F (r) + : time) derivatives. To determine the time-derivative of 2 r(1 + r + r2) r(1 + r + r2) our fields at a given point in space, we first evaluate the While the resulting metric satisfies the rr and µν com- required spatial derivatives of our fields, compute M and ponents of the Einstein equations, the rµ components of b, and then numerically solve this 5 × 5 matrix equation. the Einstein equations impose a further set of d condi- Having computed the time-derivatives, we propagate the tions. These constraints are equivalent to the conserva- solution forward in time via standard techniques. tion of the fluid stress tensor built from uµ(x) and T (x) In our numerical computations we fix periodic bound- at the corresponding order in the gradient expansion with ary conditions in both spatial directions with period a specific set of transport coefficients [1,2]. Thus, given L = 1500, with the initial temperature set to a constant 3 µ a solution u (x) and T (x) of the hydro equations of mo- T (0) = 4π . We represent all fields pseudospectrally in a tion, we can simply plug this flow into the fluid-gravity fourier basis of 306×306 plane waves, computing spatial metric equations and, upon solving a set of 1-dimensional derivatives spectrally and propagating the system for- ODEs along the radial direction, construct a numerical ward in time using Matlab's built-in general-purpose in- metric which satisfies the full Einstein equations to the tegrator, ode45. We focus on two classes of initial condi- appropriate order in the fluid gradients. tions: a superposition of the 1000 lowest-frequency plane waves with randomized amplitudes and phases; and, fol- Numerical Methods lowing [5], a line of 10 vorticity stripes generated by the 2π velocity field uy = cos(5 L x), to which we add small per- Our calculation is naturally divided into two steps.
Load more

Recommended publications
  • Exact Null Tachyons from Renormalization Group Flows
    Exact null tachyons from renormalization group flows The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Citation Adams, Allan , Albion Lawrence, and Ian Swanson. “Exact null tachyons from renormalization group flows.” Physical Review D 80.10 (2009): 106005. © 2009 The American Physical Society As Published http://dx.doi.org/10.1103/PhysRevD.80.106005 Publisher American Physical Society Version Final published version Citable link http://hdl.handle.net/1721.1/52507 Terms of Use Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. PHYSICAL REVIEW D 80, 106005 (2009) Exact null tachyons from renormalization group flows Allan Adams,1 Albion Lawrence,2 and Ian Swanson1 1Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA 2Theory Group, Martin Fisher School of Physics, Brandeis University, MS057, 415 South Street, Waltham, Massachusetts 02454, USA (Received 11 August 2009; published 20 November 2009) We construct exact two-dimensional conformal field theories, corresponding to closed string tachyon and metric profiles invariant under shifts in a null coordinate, which can be constructed from any two- dimensional renormalization group flow. These solutions satisfy first order equations of motion in the conjugate null coordinate. The direction along which the tachyon varies is identified precisely with the world sheet scale, and the tachyon equations of motion are the renormalization group flow equations. DOI: 10.1103/PhysRevD.80.106005 PACS numbers: 11.25.Àw, 11.10.Hi I.
    [Show full text]
  • Yonatan F. Kahn, Ph.D
    Yonatan F. Kahn, Ph.D. Contact Loomis Laboratory 415 E-mail: [email protected] Information Urbana, IL 61801 USA Website: yfkahn.physics.illinois.edu Research High-energy theoretical physics (phenomenology): direct, indirect, and collider searches for sub-GeV Interests dark matter, laboratory and astrophysical probes of ultralight particles Positions Assistant professor August 2019 { present University of Illinois Urbana-Champaign Urbana, IL USA Current research: • Sub-GeV dark matter: new experimental proposals for direct detection • Axion-like particles: direct detection, indirect detection, laboratory searches • Phenomenology of new light weakly-coupled gauge forces: collider searches and effects on low-energy observables • Neural networks: physics-inspired theoretical descriptions of autoencoders and feed-forward networks Postdoctoral fellow August 2018 { July 2019 Kavli Institute for Cosmological Physics (KICP) University of Chicago Chicago, IL USA Postdoctoral research associate September 2015 { August 2018 Princeton University Princeton, NJ USA Education Massachusetts Institute of Technology September 2010 { June 2015 Cambridge, MA USA Ph.D, physics, June 2015 • Thesis title: Forces and Gauge Groups Beyond the Standard Model • Advisor: Jesse Thaler • Thesis committee: Jesse Thaler, Allan Adams, Christoph Paus University of Cambridge October 2009 { June 2010 Cambridge, UK Certificate of Advanced Study in Mathematics, June 2010 • Completed Part III of the Mathematical Tripos in Applied Mathematics and Theoretical Physics • Essay topic: From Topological Strings to Matrix Models Northwestern University September 2004 { June 2009 Evanston, IL USA B.A., physics and mathematics, June 2009 • Senior thesis: Models of Dark Matter and the INTEGRAL 511 keV line • Senior thesis advisor: Tim Tait B.Mus., horn performance, June 2009 Mentoring Graduate students • Siddharth Mishra-Sharma, Princeton (Ph.D.
    [Show full text]
  • Mathematical Physics and String Theory
    TIFR Annual Report 2002-03 THEORETICAL PHYSICS String Theory and Mathematical Physics Closed String Tachyon Potential Calculation The closed string 4-Tachyon amplitude in C/ZN orbifold was calculated. In an appropriate large N limit, this will throw some light on the behaviour of closed string tachyon potential in target space. [Allan Adams, Atish Dabholkar, Ashik Iqubal, Joris Raeymaekers] Compactification by Duality Twists The Scherk-Schwarz potential generated by string theory compactifications was investigated in the case of twists belonging to the duality group. For some twists, such twisted compactifications are equivalent to introducing internal fluxes. [Atish Dabholkar, Ashik Iqubal, Prasanta Tripathy, Sandip Trivedi] Duality twists, Fluxes, and Orbifolds An important problem in string theory is to generate a potential for the unwanted massless moduli fields. With this motivation, compactifications with duality twists and their relation to orbifolds and compactifications with fluxes were investigated. Inequivalent compactifications were classified by conjugacy classes of the U-duality group and resulted in gauged supergravities in lower dimensions with nontrivial potential on the moduli space. It was shown that the potential has a stable minima precisely at the fixed points of the twist group and that the theory at the minimum has an exact CFT description as an orbifold. The implications of these results for moduli stablization is under investigation. [Atish Dabholkar with Chris Hull] Tachyon Condensation in String Theory Usually F-theory duals of string theory are considered for supersymmetric backgrounds. F- theory duals of certain nonsupersymmetric backgrounds were considered that have localized tachyons. Some speculations about the endpoint of the tachyon condensation were presented based on this duality.
    [Show full text]
  • Heating up Galilean Holography
    PUPT-2274 DCPT-08/39 Heating up Galilean holography a b b Christopher P. Herzog ∗, Mukund Rangamani †, and Simon F. Ross ‡ a Department of Physics, Princeton University, Princeton, NJ 08544, USA b Centre for Particle Theory & Department of Mathematical Sciences, Science Laboratories, South Road, Durham DH1 3LE, United Kingdom. July 7, 2008 Abstract We embed a holographic description of a quantum field theory with Galilean con- formal invariance in string theory. The key observation is that such field theories may be realized as conventional superconformal field theories with a known string theory embedding, twisted by the R-symmetry in a light-like direction. Using the Null Melvin Twist, we construct the appropriate dual geometry and its non-extremal generaliza- tion. From the nonzero temperature solution we determine the equation of state. We also discuss the hydrodynamic regime of these non-relativistic plasmas and show that the shear viscosity to entropy density ratio takes the universal value η/s = 1/4π typical of strongly interacting field theories with gravity duals. arXiv:0807.1099v3 [hep-th] 17 Oct 2008 ∗[email protected] †[email protected] ‡[email protected] 1 Introduction The AdS/CFT correspondence [1, 2, 3] maps relativistic conformal field theories holograph- ically to gravitational (or stringy) dynamics in a higher dimensional asymptotically Anti-de Sitter spacetime. As such, the correspondence is an important tool for modeling the behav- ior of strongly interacting field theories, as the dynamics on the field theory side is mapped to classical string and gravitational dynamics in the dual description. Indeed, among other achievements, this strong–weak coupling duality has improved, at least at a qualitative level, our understanding of real-time dynamics and transport properties of the quark-gluon plasma in QCD.
    [Show full text]
  • Causality, Analyticity and an IR Obstruction to UV Completion
    Published by Institute of Physics Publishing for SISSA Received: July 7, 2006 Accepted: August 24, 2006 Published: October 4, 2006 Causality, analyticity and an IR obstruction to UV completion Allan Adams,a Nima Arkani-Hamed,a Sergei Dubovsky,abc Alberto Nicolisa and Riccardo Rattazzib∗ JHEP10(2006)014 aJefferson Physical Laboratory, Harvard University, Cambridge, MA 02138, U.S.A. bCERN Theory Division, CH-1211 Geneva 23, Switzerland cInstitute for Nuclear Research of the Russian Academy of Sciences, 60th October Anniversary Prospect, 7a, 117312 Moscow, Russia E-mail: [email protected], [email protected], [email protected], [email protected], [email protected] Abstract: We argue that certain apparently consistent low-energy effective field theories described by local, Lorentz-invariant Lagrangians, secretly exhibit macroscopic non-locality and cannot be embedded in any UV theory whose S-matrix satisfies canonical analyticity constraints. The obstruction involves the signs of a set of leading irrelevant operators, which must be strictly positive to ensure UV analyticity. An IR manifestation of this restriction is that the “wrong” signs lead to superluminal fluctuations around non-trivial backgrounds, making it impossible to define local, causal evolution, and implying a surpris- ing IR breakdown of the effective theory. Such effective theories can not arise in quantum field theories or weakly coupled string theories, whose S-matrices satisfy the usual analyt- icity properties. This conclusion applies to the DGP brane-world model modifying gravity in the IR, giving a simple explanation for the difficulty of embedding this model into con- trolled stringy backgrounds, and to models of electroweak symmetry breaking that predict negative anomalous quartic couplings for the W and Z.
    [Show full text]
  • Review Panel Bios
    OCEAN EXPLORATION RESEARCH 2019 SCIENCE REVIEW PANEL OCT. 16-18, 2019 UNIVERSITY OF RHODE ISLAND GRADUATE SCHOOL OF OCEANOGRAPHY Dr. Edward J. Kearns, Panel Chair NOAA Chief Data Officer, U.S. Department of Commerce [email protected] [email protected] Dr. Edward J. Kearns is the Chief Data Officer for the US Department of Commerce, leading implementation of the Federal Data Strategy and the Foundations of Evidence Based Policy- making Act, among other initiatives. As NOAA’s first Chief Data Officer, Dr. Edward J. Kearns led the development of strategies and practices for managing NOAA’s data as a national asset. Ed is seeking to promote new uses and wider understanding of federal data through new partnerships and technologies, such as the NOAA Big Data Project. As part of the White House’s Leveraging Data as a Strategic Asset initiative, he has also led the Commercialization, Innovation, and Public Use working group towards the development of the new Federal Data Strategy. Prior to his position as NOAA’s Chief Data Officer, Ed led the Climate Data Record program and NOAA’s data archive; guided coastal ecosystem restoration projects for the National Park Service and evaluated environmental “big data” to inform Everglades restoration; and vicariously calibrated ocean products from NASA’s satellites and developed regional integrated ocean observing and data management systems as a professor at the University of Miami. Ed holds degrees in Physical Oceanography from the University of Rhode Island (Ph.D. 1996) as well as Physics and Marine Science from the University of Miami (B.S. 1990).
    [Show full text]
  • Richard Fitzpatrick Lecture Notes
    Richard Fitzpatrick Lecture Notes Georg metricizes his Yosemite finalizes connubially or nefariously after Bertrand sympathise and smudged dishearteningly, appointed and extroverted. Is Deane always heteromorphic and lamblike when dome some fogram very wetly and forwhy? Elliott galvanises his beggings pandy perforce or standoffishly after Luther tenure and insults grievingly, blowsiest and hydrobromic. As we have already seen, and as is apparent from Eq. Now customize the name of a clipboard to store your clips. Huge and overwhelming indeed, it was the starting point of this my own post. If you can enable javascript and speed when they reasoned, richard fitzpatrick lecture notes about. In principle, each photon which passes through our apparatus is equally likely to pass through one of the two slits. Enter your bank for richard fitzpatrick lecture notes about a mirror, richard fitzpatrick professor allan adams massachusetts institute for something went wrong. The lecture notes introduce quantum mechanics, potential describes selected practical physicists, richard fitzpatrick lecture notes, so under its own steam. He wrote about it that all three separate ion poloidal flow, richard fitzpatrick lecture notes for richard fitzpatrick, when light rays from your comment is. Here, E is the energy of a body, m is its mass, and c is the velocity of light in vacuum. It follows from Eqs. Press J to jump to the feed. We shall neglect both ends by richard fitzpatrick alongside andy ridley, richard fitzpatrick lecture notes. Moreover, the point at which a given photon strikes the film is not influenced by the points at which previous photons struck the film, given that there is only one photon in the apparatus at any given time.
    [Show full text]
  • Behavior of Turbulent Flow of Superfluids Is Opposite That of Ordinary Fluids 25 July 2013, by Jennifer Chu
    Behavior of turbulent flow of superfluids is opposite that of ordinary fluids 25 July 2013, by Jennifer Chu A superfluid moves like a completely frictionless translated the physics of black holes to that of liquid, seemingly able to propel itself without any superfluid turbulence, using a technique called hindrance from gravity or surface tension. The holographic duality. physics underlying these materials—which appear to defy the conventional laws of physics—has Consider, for example, a holographic image on a fascinated scientists for decades. magazine cover. The data, or pixels, in the image exist on a flat surface, but can appear three- Think of the assassin T-1000 in the movie dimensional when viewed from certain angles. An "Terminator 2: Judgment Day"—a robotic shape- engineer could conceivably build an actual 3-D shifter made of liquid metal. Or better yet, consider replica based on the information, or dimensions, a real-world example: liquid helium. When cooled found in the 2-D hologram. to extremely low temperatures, helium exhibits behavior that is otherwise impossible in ordinary "If you take that analogy one step further, in a fluids. For instance, the superfluid can squeeze certain sense you can regard various quantum through pores as small as a molecule, and climb theories as being a holographic image of a world up and over the walls of a glass. It can even with one extra dimension," says Paul Chesler, a remain in motion years after a centrifuge postdoc in MIT's Department of Physics. containing it has stopped spinning. Taking this cosmic line of reasoning, Adams, Now physicists at MIT have come up with a Chesler and colleagues used holographic duality as method to mathematically describe the behavior of a "dictionary" to translate the very well- superfluids—in particular, the turbulent flows within characterized physics of black holes to the physics superfluids.
    [Show full text]
  • The NYU Law Fund
    the new new deal Faculty and students engage in ideas for making better and more effective government. mediator in chief Ken Feinberg ’70 signs on for the impossible—again. where there’s a wilf THE MAGAZINE OF THE NEW YORK UNIVERSITY SCHOOL OF LAW | 2010 A new academic hall debuts on MacDougal Street. the GUARDIAN He has stared down drug kingpins, Wall Street CEOs, and even the Treasury secretary. How Special Inspector General Neil Barofsky ’95 is protecting the taxpayers’ $700 billion bailout fund. 1956 1961 1966 1971 1976 1981 1986 1991 1996 2001 2006 1956 1961 1966 1971 1976 1981 19 NYU School of Law Reunion Friday & Saturday.NYU April 8-9,Law 2011 Reunion PleasePlease visitvisit law.nyu.edu/reunion2011law.nyu.edu/reunion2010Friday & Saturday, for for Aprilmore more information 8–9,information 2011 A Note from the Dean As many readers know, in each year’s magazine since I became dean in 2002, we have featured an area of law in which I am confident a peer review would say we take the lead among top law schools. Past issues have highlighted our programs in international, environmental, criminal, and clinical law; legal philosophy; civil procedure; and the relatively new fields of law and democracy and law and security. This year, we feature a subject very close to my heart, administrative law and policy. “Building Good Government,” complicated, governance in master for TARP executive by Larry Reibstein, traces how the world has taken on a whole compensation reveals how he NYU School of Law became new dimension. Last year the manages unique assignments the first leading law school Law School was honored to compensating victims of 9/11, to successfully require a 1L host some of the world’s leading Agent Orange, and other disas- course that analyzes statutes scholars of global governance ters.
    [Show full text]
  • Anomaly Mediation from Unbroken Supergravity
    Anomaly mediation from unbroken supergravity The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Citation D’Eramo, Francesco, Jesse Thaler, and Zachary Thomas. “Anomaly Mediation from Unbroken Supergravity.” Journal of High Energy Physics 2013, 9 (September 2013): 125 © 2013 SISSA As Published http://dx.doi.org/10.1007/JHEP09(2013)125 Publisher Springer Berlin Heidelberg Version Final published version Citable link http://hdl.handle.net/1721.1/116053 Terms of Use Attribution 4.0 International (CC BY 4.0) Detailed Terms https://creativecommons.org/licenses/by/4.0/ Published for SISSA by Springer Received: July 29, 2013 Accepted: August 26, 2013 Published: September 24, 2013 Anomaly mediation from unbroken supergravity JHEP09(2013)125 Francesco D'Eramo,a;b Jesse Thalerc and Zachary Thomasc aDepartment of Physics, University of California, Berkeley, CA 94720, U.S.A. bTheoretical Physics Group, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, U.S.A. cCenter for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A. E-mail: [email protected], [email protected], [email protected] Abstract: When supergravity (SUGRA) is spontaneously broken, it is well known that anomaly mediation generates sparticle soft masses proportional to the gravitino mass. Re- cently, we showed that one-loop anomaly-mediated gaugino masses should be associated with unbroken supersymmetry (SUSY). This counterintuitive result arises because the un- derlying symmetry structure of (broken) SUGRA in flat space is in fact (unbroken) SUSY in anti-de Sitter (AdS) space. When quantum corrections are regulated in a way that pre- serves SUGRA, the underlying AdS curvature (proportional to the gravitino mass) neces- sarily appears in the regulated action, yielding soft masses without corresponding goldstino couplings.
    [Show full text]
  • Jhep09(2007)038
    Published by Institute of Physics Publishing for SISSA Received: June 21, 2007 Accepted: August 23, 2007 Published: September 14, 2007 Expanding F-theory JHEP09(2007)038 Matthew Kleban and Michele Redi Center for Cosmology and Particle Physics, Department of Physics, New York University, 4 Washington Place, New York, NY 10003, U.S.A. E-mail: [email protected], [email protected] Abstract: We construct a general class of new time dependent solutions of non-linear σ-models coupled to gravity. These solutions describe configurations of expanding or con- tracting codimension two solitons which are not subject to a constraint on the total tension. The two dimensional metric on the space transverse to the defects is determined by the Liouville equation. This space can be compact or non-compact, and of any topology. We show that this construction can be applied naturally in type IIB string theory to find backgrounds describing a number of 7-branes larger than 24. Keywords: F-Theory, p-branes, Sigma Models. °c SISSA 2007 http://jhep.sissa.it/archive/papers/jhep092007038 /jhep092007038.pdf Contents 1. Introduction 1 2. Construction 2 2.1 Sigma model solitons 3 2.2 CP1 4 3. F-theory revisited 5 3.1 Sen’s limit 6 3.2 Other topologies 8 JHEP09(2007)038 4. Corrections 9 5. Discussion 10 1. Introduction It is well known that point particles in pure 2+1 dimensional gravity — or relativistic codimension two objects in higher dimensional theories — generate a conical space with deficit angle α = m, where m is the mass of the particle (we set 8πGN = 1) [1].
    [Show full text]
  • Comments on the Fate of Unstable Orbifolds ✩
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector Physics Letters B 578 (2004) 215–222 www.elsevier.com/locate/physletb Comments on the fate of unstable orbifolds ✩ Sang-Jin Sin a,b a Stanford Linear Accelerator Center, Stanford University, Stanford, CA 94305, USA b Department of Physics, Hanyang University, Seoul 133-791, South Korea 1 Received 21 August 2003; accepted 9 October 2003 Editor: M. Cveticˇ Abstract We study the localized tachyon condensation in their mirror Landau–Ginzburg picture. We completely determine the decay r mode of an unstable orbifold C /Zn, r = 1, 2, 3 under the condensation of a tachyon with definite R-charge and mass by r 2 extending the Vafa’s work hep-th/0111105. Here, we give a simple method that works uniformly for all C /Zn.ForC /Zn, r where method of toric geometry works, we give a proof of equivalence of our method with toric one. For C /Zn cases, the orbifolds decay into sum of r far separated orbifolds. 2003 Elsevier B.V. Open access under CC BY license. 1. Introduction until the spacetime supersymmetry is restored. There- fore the localized tachyon condensation has geometric The study of open string tachyon condensation description as the resolution of the spacetime singular- [1] has led to many interesting consequences includ- ities. ing classification of the D-brane charge by K-theory. Soon after, Vafa [3] considered the problem in the While the closed string tachyon condensation involve Landau–Ginzburg (LG) formulation using the Mirror the change of the background spacetime and much symmetry and confirmed the result of [2].
    [Show full text]