## Overview

String theory, Quantum field theory, Quantum gravity

Quantum field theories with local gauge symmetry are building blocks of the modern theory of fundamental interactions between elementary particles. The basic example of gauge theory is Quantum Chromo Dynamics. There is an overwhelming evidence that QCD is the correct theory of strong interactions, but it has been difficult to directly use it to account for the wide variety of hadronic phenomena which is due to large value of gauge coupling at low energies. Theoretical understanding of gauge theory dynamics at large values of coupling when one cannot use the standard Feynman diagram perturbation theory is a major problem of physicsof strong interactions. One would like to be able to analytically compute the mass spectrum ofhadrons, understand properties of strongly coupled quark-gluon plasma, etc. A general aim is to develop new theoretical tools to understand strongly coupled gauge theories. Research in the last decade brought strong evidence that connection of gauge theories to string theory should be a key to solution of this strong coupling problem.

Gauge-string duality and, in particular, Anti deSitter / conformal field theory (AdS/CFT) correspondence is one of the most active directions of current work in theory of fundamental interactions. A remarkable progress was achieved towards quantitative understanding of this relation in the most symmetric case of duality between maximally supersymmetric gauge theory in flat 4 dimensions and superstring theory in curved 10-dimensional AdS5 x S5 space. One direction of our research is a detailed study of this duality from the string theory side using world-sheet methods and hidden integrability of the maximally symmetric theory. The goal is to give a first- principles proof of this duality for the spectrum of states and also to establish its validity at the level of correlation functions of conformal operators. We would like also to extend the string-theoretic approach to gauge-string duality to other less symmetric cases, corresponding, in particular, to certain non-supersymmetric conformal and supersymmetric non-conformal planar gauge theories. Apart from gauge-theory applications, complete solution of quantum superstring theory in curved AdS5 x S5 space and its close cousins should lead to important progress in many related areas of string theory and quantum field theory, e.g., in the study of flux compactifications, with applications to superstring model building and superstring cosmology.

Research Grants:

EU TMR grant "Quantum aspects of gauge theories, supersymmetry, unification" (1996-2003)

INTAS grant "Infinite Symmetries, Integrability and Superstring Theory"(1997-2000)

NATO grant “Effective actions in supersymmetric gauge theories and D-branes" (1997-2001)

INTAS grant "Strings, branes and higher-spin gauge fields" (2000-2002)

PPARC SPG Grant "String Theory and Realistic Field Theory" (1999-2002)

US Department of Energy Grant ``Progress in Fundamental String Theory" (1999-2005)

Dynasty Foundation grants (2007-2011)

SERC/PPARC/STFC UK research council rolling grants (1992-2011)

ERC Advanced Investigator Grant "Gauge theory - string theory duality: maximally symmetric case and beyond" (2012-2017) £1.68 mil Euro

## Research Student Supervision

Hoare,B

Iwashita,Y

Stepanchuk,A