This series consists of talks in the area of Superstring Theory.
Motivated by the cluster structure of two-loop scattering amplitudes in N = 4 Yang-Mills theory we define cluster polylogarithm functions. We find that all such functions of weight 4 are made up of a single simple building block associated to the A2 cluster algebra. Adding the requirement of locality on generalized Stasheff polytopes, we find that these A2 building blocks arrange themselves to form a unique function associated to the A3 cluster algebra.
I will describe progress in deriving 3d gravity directly from 2d conformal field theory at large central charge 'c'. In a large class of CFTs, using general arguments like modular invariance, crossing symmetry, and the OPE expansion, the spectrum, the entanglement entropy, and certain partition functions can be computed to leading order in a 1/c expansion.
In arXiv:0908.4052, Nekrasov and Shatashvili pointed out that the N=2 instanton partition function in a special limit of the Omega-deformation parameters is characterized by certain thermodynamic Bethe ansatz (TBA) like equations.In this talk I will present an explicit derivation of this fact as well as generalizations to quiver gauge theories. The TBA equations derived entirely within gauge theory have been proposed to encode the spectrum of a large class of quantum integrable systems. I will conclude with some remarks on this correspondence.
The principal chiral sigma model (PCSM) in 1+1 dimensions is asymptotically free and has as SU(N)-valued field with massive excitations. We have found all the exact form factors and two-point function of the Noether-current operators at large N using the integrable bootstrap program. At finite N, only the first non-trivial form factors are found, which give a good long distance approximation for the two-point function. We show how to use these new exact results to study non-integrable deformations. One example is the PCSM coupled to a Yang-Mills field.
Motivated by the connection between 4-manifolds and 2d N=(0,2) theories, we study the dynamics of a fairly large class of 2d N=(0,2) gauge theories. We see that physics of such theories is very rich, much as the physics of 4d N=1 theories. We discover a new type of duality that is very reminiscent of the 4d Seiberg duality. Surprisingly, the new 2d duality is an operation of order three. We study the low energy physics and use elliptic genus to detect dynamical supersymmetry breaking.
In this talk we will discuss how giant gravitons and their open string interactions emerge from super Yang-Mills
Theory. This is accomplished by diagonalizing the one loop dilatation operator on a
class of operators with bare dimension of order N. From the result of this diagonalization, the
Gauss Law governing the allowed open string excitations of giant gravitons is clearly
visible. In addition, we show that this sector of the theory is integrable.
theories with a U(1)_R symmetry, can be placed on a compact three manifold M
preserving some supersymmetry if and only if M admits a transversely
holomorphic foliation (THF). I will show that the partition function of the
resulting theory is independent of the metric and depends holomorphically on
the moduli of the THF. When applied to supersymmetric field theories on
manifolds diffeomorphic to S^3 and S^2 x S^1, this result explains many of the