Related papers: Perturbation Theory From Automorphic Forms

We present a one-parameter family of large $N$ disordered models, with and without supersymmetry, in three spacetime dimensions. They interpolate from the critical large $N$ vector model dual to a classical higher spin theory, towards a…

The weakly-coupled heterotic string is known to have problems of dilaton/moduli stabilization, supersymmetry breaking (by hidden-sector gaugino condensation), gauge coupling unification (or the Newton's constant), QCD axion, as well as…

String geometry theory is one of the candidates of the non-perturbative formulation of string theory. In this paper, from the string geometry theory, we derive path-integrals of perturbative superstrings on all the string backgrounds,…

We examine the question how string theory achieves a sum over bulk geometries with fixed asymptotic boundary conditions. We discuss this problem with the help of the tensionless string on $\mathcal{M}_3 \times \mathrm{S}^3 \times…

We make progress towards an analytical understanding of the regime of validity of perturbation theory for large scale structures and the nature of some non-perturbative corrections. We restrict ourselves to 1D gravitational collapse, for…

We explain how perturbative string theory can be viewed as an exactly renormalizable Weyl invariant quantum mechanics in the worldsheet representation clarifying why string scattering amplitudes are both finite and unambiguously normalized…

This is a set of lectures on the gauge/string duality and non-critical strings, with a particular emphasis on the discretized, or matrix model, approach. After a general discussion of various points of view, I describe the recent…

The modular invariant coefficient of the D^{2k} {\cal{R}}^4 term in the effective action of type IIB superstring theory is expected to satisfy Poisson equation on the fundamental domain of SL(2,Z). Under certain assumptions, we obtain the…

We address the problem of finite-size anyons, i.e., composites of charges and finite radius magnetic flux tubes. Making perturbative calculations in this problem meets certain difficulties reminiscent of those in the problem of pointlike…

We develop a self-consistent version of perturbation theory in Liouville space which seeks to combine the advantages of master equation approaches in quantum transport with the nonperturbative features that a self-consistent treatment…

A brief review of the status of duality symmetries in string theory is presented. The evidence is accumulating rapidly that an enormous group of duality symmetries, including perturbative T dualities and non-perturbative S-dualities,…

We introduce a hierarchical system of approximations for summing both conventional perturbation theory and large N vector expansions of models in quantum field theory and condensed matter physics. Each stage of the hierarchy consists of a…

In this paper, which is a revised version of the author's PhD thesis, we analyze two different applications of string theory. In the first part, we focus on four dimensional compactifications of Type II string theories preserving N=1…

The perturbative expansion of static force and potential is reanalyzed concerning its practical applicability. A well behaved perturbative prediction is given by the integration of the renormalization group equation for the coupling…

In the q-deformed theory the perturbation approach can be expressed in terms of two pairs of undeformed position and momentum operators. There are two configuration spaces. Correspondingly there are two q-perturbation Hamiltonians, one…

The `strong-coupling' perturbation theory over the inverse interaction constant $1/g$ near the nontrivial solution of Lagrange equation is formulated. The ordinary `week-coupling' perturbation theory over $g$ is described also to compare…

We identify and evaluate a class of physical amplitudes in four-dimensional N=4 superstring theory, which receive, in the weak coupling limit, contributions of order e^{-1/\lambda}, where \lambda is the type II superstring coupling…

A class of non-supersymmetric string backgrounds can be constructed using twists that involve space-time fermion parity. We propose a non-perturbative definition of string theory in these backgrounds via gauge theories with supersymmetry…

We develop convergent variational perturbation theory for quantum statistical density matrices. The theory is applicable to polynomial as well as nonpolynomial interactions. Illustrating the power of the theory, we calculate the…

We study the E-string theory on $\mathbb{R}^4\times T^2$ with Wilson lines. We consider two examples where interesting automorphisms arise. In the first example, the spectrum is invariant under the $F_4$ Weyl group acting on the Wilson line…