Rajesh Gopakumar

Research Summary: In the last year, in work with Suvankar Dutta, we studied the dynamics of weak coupling U(N) Yang-Mills theory at finite temperature. When the gauge theory is in a finite volume it exhibits a number of interesting phases and transitions between them as the temperature is varied. In the context of the AdS/CFT conjec- ture these have the interpretation as different geometries and transitions between them. We analysed the matrix model for the Polyakov loop which captures the dynamics of the weak coupling model and provided an explicit answer for the partition function for any finite N and temperature. The exact answer is in terms of a sum over representations of U(N) and captures the phase diagram of the gauge theory by exhibiting large N phase transitions. Quantitatively these are captured in terms of a Young Tableau density for the representations. Surpris- ingly, the large N saddle point configurations of this density together with that of the eigenvalue density for the polyakov loop naturally give rise to a two dimensional fermionic phase space picture for the different saddle points. This may be a useful clue for the holographic reconstruction of the geometry from the gauge theory In work with Justin David and Ayan Mukhopadhyay, we continued our investi- gation of the worldsheet duals for gauge theory four point correlation functions. We focussed on a class of correlators in the N = 4 super Yang-Mills theory which do not get any corrections as one varies the coupling. Using my earlier proposal for the worldsheet duals of large N gauge theories we found in a particular (semi- classical) limit that the correlation function has support on a one dimensional curve in the two dimensional moduli space of the worldsheet two pint functions. In special cases where this curve can be explicitly characterised we found that it satisfies the expected worldsheet property of crossing symmetry. We have also been investigating the duals to gauge theory four point functions in the so-called Regge limit of high centre of mass energy but fixed momentum transfer. We hope to be able to understand the localisation of the gauge theory correlation functions from a subspace of the Schwinger parameter space in terms of a worldsheet operator product expansion appropriate to picking out the lead- ing Regge trajectory.

Publications:

1. O. Aharony, J. David, R. Gopakumar, Z. Komargodsky and S. Razamat, Comments on worldsheet theories dual to free large N gauge theories Phys. Rev. D. 75, 106006 (2007).

1 2. S. Dutta and R. Gopakumar, Free Fermions and Thermal AdS/CFT JHEP 0803, 011 (2008).

Conference/Workshops Attended:

1. Solvay workshop on Gauge theory, String Theory and Geometry, Brussels, May 2007

2. XXVIII Brazilian National Meeting of Particles and Fields, Aguas de Lin- doia, Sep. 2007

3. Indian Strings Meeting ISM07, HRI, Allahabad, Oct. 2007

Visits to other Institutes:

1. IISER, Kolkata, Apr. 2007.

2. TIFR, Mumbai, May 2007.

3. ASICTP, Trieste, Italy, Aug. 2007.

4. Institute for Theoretical Physics, IFT, Sao Paulo, Sep. 2007.

Invited Lectures/Seminars:

1. Mini course on Extremisation Principles in Physics IISER Kolkata, Apr. 2007 (contd. from Feb, Mar.).

2. Comments on the Worldsheet Duals of Free Large N Gauge Theories. Solvay workshop on Gauge theory, String Theory and Geometry, Brussels, May 2007.

3. ICTP Prize Lecture, ASICTP, Trieste, Aug. 2007.

4. String Seminar From Fermions to AdS ASICTP, Trieste, Aug. 2007.

5. Four Lecture Series Gauge-String Duality, IFT, Sao Paulo, Sep. 2007.

6. Plenary talk, XXVIII Brazilian National Meeting of Particles and Fields, Aguas de Lindoia, Sep. 2007.

7. Free Fermions and Thermal AdS/CFT Indian Strings Meeting ISM07, HRI, Al- lahabad, Oct. 2007.

2 Other Activities:

1. Guided four VSP students, Jul./Oct./Dec. 2007.

2. Member, International Organising Committee, ICGC-Pune (Dec. 2007).

3. Member of various administrative committees.