This series consists of talks in the area of Superstring Theory.
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
In M-theory, the only AdS7 supersymmetric solutions are
AdS7 × S4 and its orbifolds. In this talk, I will describe a classification of
AdS7 supersymmetric solutions in type II supergravity. While in IIB none exist,
in IIA with Romans mass (which does not lift to M-theory) there are many new
ones. The classification starts from a pure spinor approach reminiscent of
generalized complex geometry. Without the need for any Ansatz, the method
determines uniquely the form of the metric and fluxes, up to solving a system
We study the
conformal bootstrap for 3D CFTs with O(N) global symmetry. We obtain rigorous
upper bounds on the scaling dimensions of the first O(N) singlet and symmetric
tensor operators appearing in the \phi_i x \phi_j OPE, where \phi_i is a
fundamental of O(N). Comparing these bounds to previous determinations of
critical exponents in the O(N) vector models, we find strong numerical evidence
that the O(N) vector models saturate the bootstrap constraints at all values of
In this talk, I will describe a new form of hidden simplicity in the planar scattering amplitudes of N=4 super-Yang-Mills theory, notably that the loop integrands can be expressed in dlog form. I will explain how this form arises geometrically from computing the scattering amplitudes using a holomorphic Wilson loop in twistor space. I will also describe a systematic method for evaluating such integrals and use it to obtain a new formula for the 1-loop MHV amplitude.