Integrability: From Statistical Systems to Gauge Theory

2019 ◽  
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Summer School ◽  
Condensed Matter ◽  
Theoretical Physics ◽  
Conformal Field ◽  
The Past ◽  
Background Material ◽  
Supersymmetric Gauge ◽  
Statistical Systems

This volume contains lectures delivered at the Les Houches Summer School ‘Integrability: from statistical systems to gauge theory’ held in June 2016. The School was focussed on applications of integrability to supersymmetric gauge and string theory, a subject of high and increasing interest in the mathematical and theoretical physics communities over the past decade. Relevant background material was also covered, with lecture series introducing the main concepts and techniques relevant to modern approaches to integrability, conformal field theory, scattering amplitudes, and gauge/string duality. The book will be useful not only to those working directly on integrablility in string and guage theories, but also to researchers in related areas of condensed matter physics and statistical mechanics.

scholarly journals Toward AGT for Parabolic Sheaves

2020 ◽  
Author(s):  
Andrei Neguţ
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Conformal Field Theory ◽  
Moduli Spaces ◽  
Type A ◽  
Conformal Field ◽  
Toroidal Algebra ◽  
Agt Correspondence ◽  
K Theory ◽  
The Ideal

Abstract We construct explicit elements $W_{ij}^k$ in (a completion of) the shifted quantum toroidal algebra of type $A$ and show that these elements act by 0 on the $K$-theory of moduli spaces of parabolic sheaves. We expect that the quotient of the shifted quantum toroidal algebra by the ideal generated by the elements $W_{ij}^k$ will be related to $q$-deformed $W$-algebras of type $A$ for arbitrary nilpotent, which would imply a $q$-deformed version of the Alday-Gaiotto-Tachikawa (AGT) correspondence between gauge theory with surface operators and conformal field theory.

scholarly journals Aspects of emergent symmetries

2016 ◽  
Vol 31 (10) ◽  
pp. 1630009 ◽  
Author(s):  
Pedro R. S. Gomes
Keyword(s):  
Field Theory ◽  
Statistical Mechanics ◽  
Degrees Of Freedom ◽  
Condensed Matter ◽  
Lorentz Invariance ◽  
Low Energy ◽  
Background Material

These are intended to be review notes on emergent symmetries, i.e. symmetries which manifest themselves in specific sectors of energy in many systems. The emphasis is on the physical aspects rather than computation methods. We include some background material and go through more recent problems in field theory, statistical mechanics and condensed matter. These problems illustrate how some important symmetries, such as Lorentz invariance and supersymmetry, usually believed to be fundamental, can arise naturally in low-energy regimes of systems involving a large number of degrees of freedom. The aim is to discuss how these examples could help us to face other complex and fundamental problems.

scholarly journals a-MAXIMIZATION IN ${\mathcal N}=1$ SUPERSYMMETRIC Spin(10) GAUGE THEORIES

2010 ◽  
Vol 25 (31) ◽  
pp. 5595-5645
Author(s):  
TERUHIKO KAWANO ◽  
FUTOSHI YAGI
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Conformal Field Theory ◽  
Gauge Theories ◽  
Unitarity Bound ◽  
Conformal Field ◽  
Coulomb Phase ◽  
Vector Representations ◽  
Chiral Superfields

A summary is reported on our previous publications about four-dimensional [Formula: see text] supersymmetric Spin(10) gauge theory with chiral superfields in the spinor and vector representations in the non-Abelian Coulomb phase. Carrying out the method of a-maximization, we studied decoupling operators in the infrared and the renormalization flow of the theory. We also give a brief review on the non-Abelian Coulomb phase of the theory after recalling the unitarity bound and the a-maximization procedure in four-dimensional conformal field theory.

Statistical Field Theory

2020 ◽  
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Field Theory ◽  
Form Factors ◽  
Theoretical Physics ◽  
Quantum Field Theories ◽  
Boundary Field ◽  
Conformal Field ◽  
Statistical Field ◽  
Statistical Field Theory ◽  
Substantial Progress ◽  
Theoretical Physicist

This book is an introduction to statistical field theory, which is an important subject within theoretical physics and a field that has seen substantial progress in recent years. The book covers fundamental topics in great detail and includes areas like conformal field theory, quantum integrability, S-matrices, braiding groups, Bethe ansatz, renormalization groups, Majorana fermions, form factors, the truncated conformal space approach and boundary field theory. It also provides an introduction to lattice statistical models. Many topics are discussed at a fairly advanced level but via a pedagogical approach. In particular, the book presents in a clear way non-perturbative methods of quantum field theories that have become decisive tools in many different areas of statistical and condensed matter physics, and which are currently an essential foundation of the working knowledge of a modern theoretical physicist.

scholarly journals Modern topics in theoretical nuclear physics

2007 ◽  
Vol 85 (3) ◽  
pp. 219-230 ◽  
Author(s):  
B K Jennings ◽  
A Schwenk
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Nuclear Physics ◽  
Condensed Matter ◽  
Effective Field ◽  
Low Energy ◽  
Many Body ◽  
The Past ◽  
Nuclear Systems ◽  
Low Energy Nuclear Physics

Over the past five years there have been profound advances in nuclear physics based on effective field theory and the renormalization group. In this review, we summarize these advances and discuss how they impact our understanding of nuclear systems and experiments that seek to unravel their unknowns. We discuss future opportunities and focus on modern topics in low-energy nuclear physics, with special attention on the strong connections to many-body atomic and condensed-matter physics, as well as to astrophysics. This makes it an exciting era for nuclear physics. PACS Nos.: 21.60.–n, 21.30.Fe

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