Quantum Fields and Strings

In this talk, I will describe recent work in string phenomenology from the perspective of computational algebraic geometry. I will begin by reviewing some of the long-standing issues in heterotic model building and the goal of producing realistic particle physics from string theory. This goal can be approached by creating a large class of heterotic models which can be algorithmically scanned for physical suitability. I will outline a well-defined set of heterotic compactifications over complete intersection Calabi-Yau manifolds using the monad construction of vector bundles. Further, I will describe how a combination of analytic methods and computer algebra can provide efficient techniques for proving stability and calculating particle spectra.

To realize massive pions, I propose a variation of the holographic model of massless QCD using the D4/D8/D8bar-brane configuration proposed by Sakai and Sugimoto. The deformation breaks the chiral symmetry explicitly and I compute the mass of the pions and vector mesons. The observed value of the pion mass can be obtained. I also argue a chiral perturbation corresponding to the deformation.

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.