String correlators on AdS3: three-point functions

We revisit the computation of string worldsheet correlators on Euclidean AdS3 with pure NS-NS background. We compute correlation functions with insertions of spectrally flowed operators. We explicitly solve all the known constraints of the model and for the first time conjecture a closed formula for three-point functions with arbitrary amount of spectral flow. We explain the relation of our results with previous computations in the literature and derive the fusion rules of the model. This paper is the first in a series with several installments.

DGLA Dg and BV formalism

Differrential Graded Lie Algebra Dg was previously introduced in the context of current algebras. We show that under some conditions, the problem of constructing equivariantly closed form from closed invariant form is reduces to construction of a representation of Dg. This includes equivariant BV formalism. In particular, an analogue of intertwiner between Weil and Cartan models allows to clarify the general relation between integrated and unintegrated operators in string worldsheet theory.

S matrix for a three-parameter integrable deformation of AdS3 × S3 strings

We consider the three-parameter integrable deformation of the AdS3 × S3 superstring background constructed in arXiv:1811.00453. Working on the string worldsheet in uniform lightcone gauge, we find the tree-level bosonic S matrix of the model and study some of its limits.

Correlation functions of symmetric orbifold from AdS3 string theory

The paper examines correspondence among correlation functions of symmetric orbifold and string theory on AdS3 described by sl(2) Wess-Zumino-Novikov-Witten (WZNW) model. We start by writing down n-point function of twist operators in the symmetric orbifold in terms of the data of effective Riemann surface. It is then shown that the correlation function can be reproduced from the sl(2) WZNW model. The computation is based on the claim that string worldsheet is given by the same Riemann surface and the reduction method from sl(2) WZNW model to Liouville field theory. We first consider the genus zero surface and then generalize the analysis to the case of generic genus. The radius of AdS3 is related to the level k of the WZNW model. For k = 3, our result should be an important ingredient for deriving AdS3/CFT2 correspondence with tensionless superstrings to all orders in string perturbation theory. For generic k, relations involving specific forms of correlation functions for strings on AdS3× X were obtained.

Worldsheets in holography: Computing corrections to the Veneziano amplitude

We provide a brief summary of a method to calculate improvements to the Veneziano amplitude, creating sub-leading nonlinearities in the Regge trajectory of states. We formulate it as an extension of a computation by Makeenko and Olesen. We begin in a confining gauge theory coupled to matter, rewriting the meson scattering amplitude as a specific path integral over shapes and sizes of closed Wilson loops using the worldline formalism. We then prescribe how to further the computation at strong coupling by employing holography, which provides a prescription for the expectation value of these Wilson loops in strongly coupled regimes. The computation we desire then appears to subsume to a certain calculation in the effective field theory of a string worldsheet embedded in a certain broad class of allowed holographic backgrounds. A convenient interaction picture presents itself naturally in this context, allowing us to draw Feynman diagrams corresponding to the first few corrections due to weaker coupling regimes. The answer we find has qualitatively the same features as other endeavors with the same objective.

Holographic Aspects of Chaos and Integrability in String- and M-Theory

In this thesis we investigate classical integrability of the string worldsheet on different super-gravity backgrounds. We focus in particular on the class of half-supersymmetric AdS7 solutions of Massive Type IIA supergravity, that are thought to be the near-horizon limit of a D6-D8-NS5 Hanany-Witten brane set-up, and are dual to six-dimensional conformal field theories with N = (1, 0) supersymmetry. We use both analytical and numerical methods to show the (bosonic sector of the) string worldsheet is non-integrable on most of these backgrounds. The backgrounds on which the string is integrable are an infinite massless solution (corresponding to an infinite constant quiver), and a background corresponding to an infinite linear quiver theory.In addition we find that the (bosonic sector of the) string is integrable on a background that we call AdS7 × (S3)λ. For this background we show that it corresponds to a 6d SCFT with an infinitely long quiver with an infinite number of flavour groups, all proportional to the colour groups. We study this particular supergravity background in detail, and suggest it corresponds to the large-N limit of the dual SCFT in the limit where the Chern-Simons level k goes to infinity.This integrable AdS7 × (S3)λ background can be obtained as the λ-deformation of AdS7×S3. In this context we study integrable deformations of supergravity backgrounds in the last part of this thesis, in particular non-Abelian T-duality. We present another back-ground on which the string is integrable by performing two non-Abelian T-dualities on two three-spheres inside the AdS5×S5 solution and study the resulting background.