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Ashoke Sen and S-Duality Winner of Fundamental Physics Prize

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GENERAL ¨ ARTICLE Ashoke Sen and S-Duality Winner of Fundamental Physics Prize Dileep Jatkar The Fundamental Physics Prize Foundation de- clared names of nine scientists in a varietyof ar- easof theoreticalphysicsas recipients of the Fun- damentalPhysicsPrize.Thisarticle is a quick introduction to Ashoke Sen's scienti¯c achieve- ments. In addition, this article containssome discussion of his S-duality proposal and the Sen Dileep Jatkar is a conjecture, which fetched him the Fundamental Professor at Harish- Physics Prize. Chandra Research Institute, Allahabad. He works in theoretical physics and his area of interest is string theory. The poor man says,\O King, both of us are Loknath; while I am theone whose masters are thepeople, you are master of thepeople". 1. Citation of the FundamentalPhysics Prize The year 2012 marks the beginning of the Fundamen- talPhysicsPrizefounded by Russianentrepreneur Yuri Milner. In the inauguralyear the Foundation announced a list of nine recipients for their outstanding contribu- tion to various disciplines in theoreticalphysics.Asper their website, http://fundamentalphysicsprize.org, TheFundamental Physics Prize recognizes transforma- tive advances in the ¯eldof fundamental physics ... in- cluding advances in closelyrelated ¯elds with deep con- nections tophysics. Ashoke Sen, a professor attheHarish-Chandra Research Keywords Institute, Allahabad, India is one of the nine recipients Fundamental Physics Prize of this Prize. The citation for which he is awarded this 2012, S-duality, Sen conjecture. RESONANCE ¨ April 2013 323 GENERAL ¨ ARTICLE Ashoke Sen prize (asstated onthewebsite) is received the [Ashoke Sen is awarded the Fundamental Physics Prize] Fundamental for uncovering strikingevidenceof strong-weakduality Physics Prize for in certain supersymmetric string theories andgauge the- providinga ories,opening thepath to therealization that all string definitiveevidence theories are di®erent limits of the same underlying in favour of S- theory. duality. Other recipients of the FundamentalPhysicsPrizeare: Nima Arkani-Hamed, JuanMaldacena,NathanSeiberg, Edward Witten all from Institute for Advanced Study, Princeton, USA, AlanGuth from MIT,Boston,USA, Andre Linde from Stanford University, Stanford, USA, Alexei Kitaev fromCalTech,Pasadena,USAand Maxim Kontsevich from IHES, France. It would perhaps be appropriate to say thattheFundamentalPhysicsPrize hasbecomeprestigious solely due to the stature of these inauguralrecipients. Certainly each of these recipients is a stalwart in his Ashoke Sen ¯eld of interest but it will not be anexaggeration to say thatAshokeSen being one of the recipients hasgiven further credence to the Prize. It is not becauseheisthe only Indianinthelistof recipients butbecause of his phenomenal achievements in string theory. He hasbeen spearheading severalnewdevelopments in string theory for over two decades. As mentioned above, Sen received this award for his work on strong{weakduality(also known asS-duality), which he did in the early 1990s, with a de¯nitive evi- dence for such a duality being provided by him in Febru- ary 1994. In additiontothis,someof his pioneering works include, formulation of string theory in background ¯elds, classi¯cation of conformal¯eld theories, string ¯eld theory (for open strings aswellas closed strings), tachyon condensation, and anenormousbodyof work on developing understandingof a class of black holes in string theory. Clearly it would be impossible to give even 324 RESONANCE ¨April 2013 GENERAL ¨ ARTICLE a °avour of some of these works in this article. We will During PhD and therefore restrict ourselves to a discussion of S-duality, post-doctoral the work cited for the Prize. However, I cannot resist fellowship he did giving a not-so-brief account of Ashoke Sen's academic pioneering work on timeline! QCD, grand 2. Tracing Academic Worldline unified theories, magnetic Ashoke Sen studied up to his matriculation in Shailendra monopoles and SircarVidyalaya in Calcutta (Kolkata). He obtained his string theory. Bachelor of Science (BSc) degree from Presidency Col- lege, Calcutta. He then joined the IndianInstitute of Technology, Kanpur, where he got his Masters degree in Physics. After that, he went to the State University of New York, Stonybrook, USA (now Stonybrook Uni- versity) to pursue his PhD. Here he worked under the guidance of George Sterman, who hadthenjustjoined the Institute for TheoreticalPhysics,Stonybrook, as a faculty and was working on QCD, the theory of strong interactions. Sen worked on QCD during his PhD, which wasentirelybasedonworkdoneall by himself.Ibelieve his ¯rst work, an80-page manuscript on `Asymptotic be- havior of the Sudakov form-factor in QCD',byitself was good enough to ful¯l the requirement of a PhD degree. It was a thorough study of a certain classof logarith- miccorrectionsinQCD,whoseimportance wasbetter appreciated by the QCD community almost a decade later. Sen then took up a post-doctoralposition atFermilab, Batavia, USA. During this period he worked on a va- riety of subjects and wrote about 23 papers within a spanof three years. This, in my opinion, was more of anexploratory period during which he worked on QCD, magnetic monopoles and their implications onproton stability, grand uni¯ed theories, supergravity, and string theory, which he worked on towards the end of his stay in Fermilab. His pioneering work on `The heterotic string in arbitrary background ¯eld 'was just the declaration of RESONANCE ¨ April 2013 325 GENERAL ¨ ARTICLE Ever since his his arrival in the ¯eld of string theory. After completing return to India, his post-doctoralpositionatFermilab hejoinedSLAC, Ashoke Sen has Menlo Park, USA where he spent a littlemorethantwo been an years. This was another period of proli¯cworkbutwas undisputed leader quite unlike thatinFermilab. By now hehadmade up in the field of string hismindtoworkinstring theory and all his 20 publica- tions from SLAC are onvarious aspects of string theory. theory. While severalof them are important contributions, con- ditions on space-time supersymmetry on the heterotic string compacti¯cations and analysis of various issues in string perturbation theoryhave had a lasting impact on the ¯eld. After spending two years at SLAC, Sen joined the fac- ulty of TIFR atMumbai. His work in TIFR canbe broadly classi¯ed into three parts: Study and classi¯cation of rationalconformal¯eld theories;² Alarge body of workonstring ¯eld theory; ² Duality symmetries in string theory. ² It is the programme of studying duality symmetries, which fetched him the FundamentalPhysics Prize. There are di®erent kinds of duality symmetries in string theory. It mayseemodd to use bothduality and symmetry at the same time; however, string theory hascertain inter- esting properties due to which a single phenomenon has two descriptions. These dual descriptions are not dis- tinguishable for a low energy observer. Among a variety of dualities, strong{weakduality is one thatismoredif- ¯cult to understand. This is because it relates a weakly coupled theory to a strongly coupled theory. While one has better controlovercomputations in the weakly cou- pled theory, computations in the strong coupling limit are notoriously di±cult. We will see below the trick employed by Ashoke Sen, of studying a specialclass of states, called the BPSstates, to gain insight into this symmetry. 326 RESONANCE ¨April 2013 GENERAL ¨ ARTICLE After spending about seven and a half years in TIFR, Ashoke Sen moved to Harish-Chandra Research Insti- tute (HRI) (atthattimeknownasMehta Research Insti- tute of Mathematics and MathematicalPhysics),Alla- habad. His work on duality symmetries in string theory hadjustledtowhatisnowcalled `the second super- stringrevolution'. However, change of locationhadno adverse impact on research output. For example, some of his early works in HRI are now known as`The Sen limit of F-theory', `The Sen four manifolds' and `Sen{ Seiberg de¯nition of Matrix theory'. Althoughhewas the one who convinced the string theory community to pay attention to the spectrum of BPS states, he started focussing his attention on non-BPS states! In a series of papers on tachyon condensation and non-BPS states, he convinced the community thatthereismore interesting physics hidden there, just when most of thecommunity hadbarely begun to appreciate the importanceof BPS states. The work on tachyon condensation and its un- derstanding in terms of a new formulation of string ¯eld theory was followed by another big programme of un- derstanding entropy of a specialclass of black holes in string theory. A programme which is still being pursued! 3. S-duality We now focus our attentionontheS-duality.Before we get into the technicaldetails let us take a semi-technical tour of the implications of S-duality. Action of the S- duality transformation takes us from a strongly coupled description of one theory to a weakly coupled descrip- tion of another theory. A coupling parameter in a theory is a measure of how constituents of the theory interact with each other. If this parameter is small, then con- stituents are weakly interacting but if this parameter is large, then they are strongly interacting. There are techniques like perturbation theory which give reliable results if the coupling parameter is small, orequiva- lently if the theory is weakly coupled, but this technique RESONANCE ¨ April 2013 327 GENERAL ¨ ARTICLE S-duality relates fails miserably if the theory is not weakly coupled. If S- strongly coupled duality transformationrelated a strongly
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