Rajesh Gopakumar

Research Summary:

In the last year I have studied a number of issues relating to the correspondence between gauge theories and string theories.

In 2002 some more progress was made in understanding the duality between gauge theories and string theories when it was recognised that string theories in the Penrose (or PP-wave) limit of Anti De Sitter space times can be solved at the classical level. Moreover these geometries were conjectured to be the dual description of Super Yang-Mills theory in a particular sector with large quantum numbers. An important question is to understand string interactions in this theory. I approached this problem from the viewpoint of relating it to a Matrix description via certain string dualities. This enabled me to obtain scaling relations that determined the effective strength of string interactions in this background. This effective coupling nicely interpolates between the behaviour expected in various parameter regimes.

Another problem I studied involved the intriguing observation by Dijkgraaf and Vafa relating the dynamics of gauge theories to those of simple zero dimensional matrix models. This seemed to indicate that some aspects of the quantum gauge theory could be easily captured by the saddle point of the Large matrix model. This seemed like a realisation of the old idea of a Master field description for at least a sector of the gauge theory. I showed for a certain set of holomorphic quantities in the gauge theory that the master field that reproduced them was related in a precise way to (but not the same as) that of the matrix model.

I have recently been studying the possibility that the idea of dual gravitational description of gauge theories might also extend to free field theories. This would be very striking as it would give us the oppurtunity to understand in this simple field theory how exactly an extra dimension emerges with gravitational dynamics. I have made some progress in identifying this mechanism which will be reported on shortly.

Publications:

1. R. Gopakumar, ``String interactions in PP-waves,'' Phys. Rev. Lett. 89, 171601 (2002)

2. R. Gopakumar, M. Headrick and M. Spradlin, ``On noncommutative multi-solitons,'' Commun. Math. Phys. 233, 355 (2003).

3. R. Gopakumar, ``N = 1 theories and a geometric master field,'' JHEP, 05, 033, (2003).

Conference/Workshops Attended:

1. School on String Theory, Shiraz, Iran, Apr. 20-28, 2002. 2. Workshop on String theory, HRI, Dec. 2002. 3. ``Theoretical Physics 2003'', Indian Association of Cultivation of Science, Kolkata, Jan. 2003 4. String Theory workshop, IACS, Kolkata, Jan. 2003. 5. Stanford-Weizmann workshop on String Theory, Stanford University, USA, Feb. 2003.

Visits to other Institutes:

1. TIFR, Mumbai, (Apr. 15-20, July 25-Aug.1, 2002). 2. Institute for Advanced Study, Princeton, USA, (May-July, 2002). 3. Stanford University, USA, (Jan.29-Feb.8, 2003). 4. Harvard University, USA (mid-June, 2002, Mar. 18-Apr.13, 2003).

Invited Lectures/Seminars:

1. 4 Lectures on PP-waves (April, 2002), 4 lectures on the Dijkgraaf-Vafa conjecture (July,2002), TIFR, Mumbai. 2. 4 lectures at Shiraz school on String Theory, Shiraz, Iran, (Apr. 2002). 3. Colloquium, Dept. of Mathematics, TIFR, Mumbai, (Apr. 2002). 4. Seminar, RRI, Bangalore (July, 2002). 5. Seminar, JNU, New Delhi, (Nov. 2002). 6. Lecture at ``TP2003'', IACS, Kolkata and seminar at workshop on String theory, IACS, Kolkata. 7. Seminar, SW workshop on String theory, Stanford University, (Feb. 2003). 8. Seminar, Caltech, USA, (Feb. 2003). 9. 9 Lectures at SERC School, IIT Chennai (Feb. 2003).

Other Activities:

Was one of the organisers of the ``Workshop on String Theory'', HRI, Dec. 2003.