Related papers: Perturbation Theory From Automorphic Forms

We analyze perturbative aspects of gauged matrix models, including those where classically the gauge symmetry is partially broken. Ghost fields play a crucial role in the Feynman rules for these vacua. We use this formalism to elucidate the…

We present simple models which exhibit some of the remarkable features expected to hold for the as yet unknown non-perturbative formulation of string theories. Among these are: (a) the absence of a background or embedding space for the full…

Using the general argument in Borel resummation of perturbation theory that links the divergent perturbation theory to the nonperturbative effect we argue that the nonperturbative effect associated with the perturbation theory should have a…

We propose a manifestly U-duality invariant modular form for the D^4 R^4 interaction in type IIB string theory compactified on T^2. It receives perturbative contributions upto two loops, and non-perturbative contributions from D-instantons…

Type 0A string theory in the (2,4k) superconformal minimal model backgrounds and the bosonic string in the (2,2k-1) conformal minimal models, while perturbatively identical in some regimes, may be distinguished non-perturbatively using…

We confront the problem of giving a fundamental definition to perturbative string theory in spacetimes with totally compact space (taken to be a torus for simplicity, though the nature of the problem is very general) and non-compact time.…

We use a combination of a 't Hooft limit and numerical methods to find non-perturbative solutions of exactly solvable string theories, showing that perturbative solutions in different asymptotic regimes are connected by smooth interpolating…

Using a world-sheet covariant formalism, we derive the equations of motion for second order perturbations of a generic macroscopic string, thus generalizing previous results for first order perturbations. We give the explicit results for…

We compare the non-linear matter power spectrum in real space calculated analytically from 3rd-order perturbation theory with N-body simulations at 1<z<6. We find that the perturbation theory prediction agrees with the simulations to better…

These lectures provide an introduction to perturbative string theory and its construction on spaces with background Ramond flux. Traditional covariant quantization of the string and its connection with vertex operators and conformal…

We obtain the exact non-perturbative thresholds of $R^4$ terms in IIB string theory compactified to eight and seven dimensions. These thresholds are given by the perturbative tree-level and one-loop results together with the contribution of…

The solution term by term to the scattering of all consistent string theories is given. The moduli space of M-theory is derived and connects the various string theories. The solutions contain both the perturbative and non-perturbative…

The role of integrable systems in string theory is discussed. We remind old examples of the correspondence between stringy partition functions or effective actions and integrable equations, based on effective application of the matrix model…

We construct the ordinary irreducible representations of the group of automorphisms of a finite rooted tree and we get a natural parametrization of them. To achieve this goals, we introduce and study the combinatorics of tree compositions,…

We consider the two-dimensional quantum field theory of a scalar field self-interacting via two periodic terms of frequencies $\alpha$ and $\beta$. Looking at the theory as a perturbed Sine-Gordon model, we use Form Factor Perturbation…

We describe a construction of cocyclic perturbations of the semigroup of shifts on the semiaxis by means of the theory of model spaces. It is shown that one can choose an inner function that determines the model space so that the elements…

In quantum mechanics and quantum field theory perturbation theory generically requires the inclusion of extra contributions non-perturbative in the coupling, such as instantons, to reproduce exact results. We show how full non-perturbative…

In this contribution to the Proceedings of the Conference on Analysis, Complex Geometry, and Mathematical Physics, an expository overview of superstring perturbation theory to two loop order is presented to an audience of mathematicians and…

The conditions for the cancellation of all gauge, gravitational, and mixed anomalies of $N=1$ supersymmetric models in six dimensions are reviewed and illustrated by a number of examples. Of particular interest are models that cannot be…

Conformal boundary conditions in two-dimensional conformal field theories are still mostly an uncharted territory. Even less is known about the relevant boundary deformations that connect them. A natural approach to the problem is via…