Quantum Fields and Strings

Abstract: This group of astronomical order is slowly yielding its secrets.It is the symmetry group of a rational conformal field theory. In thisintroductory talk, I will discuss the functions that constitute monstrousmoonshine and explain the importance of the monster group and itsconnections with better established parts of mathematics

We discuss D-brane instantons in four-dimensional string compactifications with special emphasis on Eucliden D2-branes in Type IIA orientifolds with spacetime filling D6-branes. These can induce superpotential couplings among the open string fields which are forbidden at the perturbative level since they violate some of the global U(1) symmetries generically present in string theory. Phenomenologcially important couplings of this type include Majorana mass terms for right-handed neutrinos or mu-terms in the Higss sector of the MSSM. If realized in concrete constructions, the exponential suppression of such non-perturbative terms may 'naturally' generate the observed hierarchies characteristic of these couplings. After discussing the general philosophy, we derive the prescription for the CFT computation of such non-perturbative superpotential couplings and exemplify the computation of Majorana mass terms in toroidal intersecting brane worlds. If time permits, we also comment on D2-instanton effetcs potentially destabilising the vacuum or modifying the D-term supersymmetry conditions.

After reviewing recent developments in the study of the AdS/CFT correspondence between the IR gauge theory living on a stack of D3-branes placed at a Calabi-Yau singularity and type IIB string theory on the near horizon geometry, we focus on the problem of counting chiral BPS operators in this class of CFTs and we match them with the dual string states in the general case of toric CY. Partition functions can be explicitly written in all sectors with fixed baryonic charge using localization over fixed points of the toric actions. These partition functions are related to the volume functions of the Sasaki-Einstein manifold and of its divisors.

Light-cone superstring field theory (LCSFT) and matrix string theory (MST) are closely related. Both theories at the tree level are the Green-Schwarz superstring theory in the light-cone gauge. At the interaction level, the twist fields and the spin fields in MST correspond to the string interaction vertices in LCSFT. Since the CFT fields in MST are characterized by their OPEs, we would like to realize the OPEs by the interaction vertices in LCSFT to see the correspondence. In this talk I will begin with reviews of both theories and proceed to the correspondence between them.

The duality between theories of quantum strings and Yang-Mills gauge theories, in particular the AdS/CFT conjecture, has over the years given rise to many important physical insights. Recently, the realization that both sides of the duality, in certain limits, can be be described by integrable systems has lead to a good deal of progress. In this talk we will review the construction of these integrable structures and their usefulness in understanding strings in curved backgrounds/strongly coupled gauge theories. We will discuss how the asymptotic S-matrix that enters the Bethe equations for gauge theory anomalous dimensions provides a very convenient description of the system and how it can be reproduced from the classical string theory. Further, we will outline some partial attempts to extend this equivalence, and the corresponding integrable structures, to include world-sheet quantum loop effects.

The exact boundary states for the rolling D-brane solution in two-dimensional black hole systems will be presented.I will study the physical significance of the solution in relation to the ``tachyon-radion correspondence\" and the ``black hole - string transition\". When the alpha\' corrections become larger, when at the same time the Hawking temperature coincide with the Hagedorn temperature, the phase transition occurs and the physics changes drastically. It also suggests the universal feature of the decaying D-brane and its failure in the strong quantum regime. The talk is based on my series of works hep-th/0605013, hep-th/0507040 in collaboration with Soo-jong Rey (SNU) and Yuji Sugawara (Tokyo).

I will discuss some ambiguities involved in using the AdS/CFT correspondence to calculate the ultra-relativistic jet quenching parameter for quarks moving in an N=4 super Yang-Mills thermal bath. Along the way, I will investigate the behavior of various string configurations on a five-dimensional AdS black hole background.