Ashoke Sen

Research Summary:

The main theme of my research during 2003-04 has been on the understanding of the dynamics of open string theory on unstable D-branes and the relation between open and closed string description of various physical processes. In particular by carefully comparing the results based on open string and closed string calculations I argued that the classical open string results on the decay of unstable D-branes in string theory provide dual description of the closed string state into which the D-brane decays. This gave rise to a new type of open-closed string duality conjecture according to which tree level open string theory can contain information about the closed string theory. This conjecture was put on a firm footing by testing it in the context of two dimensional string theory. In this case the theory can be mapped to a theory of free non-relativistic fermions moving under the influence of an inverted harmonic oscillator potential, and is exactly solvable. One sees that in this theory the open-closed duality conjecture reduces to the statement of equivalence between a bosonic and a fermionic field in two dimensions.

A better understanding of the open-closed string duality in critical string theory undoubtedly requires a better understanding of the dynamics of open string theory on unstable D-brane systems. Keeping this in view I studied the role of conservation laws in the study of open string dynamics and constructed infinite set of conserved charges which characterize time dependent classical solutions on an unstable D-brane. In two dimensional string theory these charges can be identified as appropriate linear combinations of the infinite set of conserved charges which are known to exist for the inverted harmonic oscillator system. We also developed a general method for constructing the energy-momentum tensor of a non-local field theory and applied it to construct the energy-momentum tensor of open string field theory.

Although open string field theory is required for describing the complete dynamics of unstable D-branes, an effective field theory with square root type action seems to capture qualitatively many aspects of the dynamics of this system. We provide further evidence for this by showing that it reproduces the qualitative features of the moduli space of classical solutions in this theory. We also use this effective action, coupled to gravity, to examine possible cosmological consequences of the evolution of the tachyon and construct non-singular cosmological solutions with a bounce. Although these solutions require fine tuning of initial conditions from the closed string viewpoint, we argue that this may be natural from the open string viewpoint.

Publications:

• A. Sen, "Open and closed strings from unstable D-branes," Phys. Rev. D 68, 106003 (2003) [arXiv:hep-th/0305011].

• A. Sen, "Open-closed duality at tree level," Phys. Rev. Lett. 91, 181601 (2003) [arXiv:hep-th/0306137].

• A. Sen, "Open-closed duality: Lessons from matrix model," Mod. Phys. Lett. A 19, 841 (2004) [arXiv:hep-th/0308068].

• A. Sen, "Moduli space of unstable D-branes on a circle of critical radius," JHEP 0403, 070 (2004) [arXiv:hep-th/0312003].

• A. Sen, "Remarks on tachyon driven cosmology," arXiv:hep-th/0312153.

• A. Sen, "Rolling tachyon boundary state, conserved charges and two dimensional string theory," JHEP 0405, 076 (2004) [arXiv:hep-th/0402157].

• A. Sen, "Energy momentum tensor and marginal deformations in open string field theory," arXiv:hep-th/0403200.

Courses Given:

• Spring, 2003: Quantum Field Theory 1

• Fall, 2003: Quantum Field Theory 2

• Spring, 2004: Quantum Field Theory 1

Distinctions:

Awarded D.Sc. (Hon.) by Calcutta University

Technical talks at conferences / schools:

• Tachyon dynamics in open string theory, 4 lectures at ICTP SpringSchool On Superstring Theory And Related Topics, 31 Mar - 8 Apr 2003, Trieste, Italy

• Tachyon dynamics in open string theory, 4 lectures at the Theoretical Advanced Study Institute In Elementary Particle Physics (TASI 2003): Recent Trends In String Theory, 1-27 Jun 2003, Boulder, Colorado

• Closed Strings and Unstable D-Branes, Strings 2003, July 6-11 2003, Kyoto, JAPAN.

• Tachyon dynamics in open string theory, 4 lectures at the Summer School on Strings, Gravity and Cosmology, July 14-25, 2003, PIMS at the University of British Columbia Vancouver, Canada.

• Tachyon dynamics in open string theory, 4 lectures at the IPM String School And Workshop 2003, 29 Sep - 9 Oct 2003, Caspian Sea, Iran

• Dynamics of D-brane decay, Nobel Symposium 2003, Cosmology and String Theory, August 14-19, 2003, Sigtuna, Sweden

• Tachyons in string theory, 4 lectures at the 3rd ICTP Latin American String School (LASS 2003), 1-19 Dec 2003, Sao Paulo, Brazil

• Review of Tachyon Condensation, National Workshop on String Theory, IIT Kanpur, December 8 - 21, 2003

• Time dependent classical solutions in open string theory, 2 lectures at the Spring School on Superstring Theory and Related Topics, 15-23 Mar 2004, Trieste, Italy

Endowment lectures / General Lectures:

• Search for a unified theory (4 lectures), Popli memorial lectures at the St. Stephen's College, Delhi, Nov. 17-20, 2003.

• Search for a unified theory, Special lecture at the Guwahati meeting of the Indian Academy of Sciences, 21-23 Nov. 2003.

• Search for a unified theory, B.B. Roy memorial lecture at Calcutta University, 24 Nov 2003

• Search for a unified theory, Subhashis Nag memorial lecture, IMSc. Chennai, Nov. 29, 2003.

• Search for a unified theory, 8th Public Lecture of the TIFR Alumni Association, TIFR, Mumbai, Feb 27, 2004.

• Search for a unified theory, Public lecture at the National Chemical Laboratory, Pune, Feb 28, 2004.