scholarly journals Two-loop rational terms in Yang-Mills theories

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Jean-Nicolas Lang ◽  
Stefano Pozzorini ◽  
Hantian Zhang ◽  
Max F. Zoller
Keyword(s):  
Scattering Amplitudes ◽  
Gauge Theories ◽  
A Posteriori ◽  
Four Dimensions ◽  
Yang Mills ◽  
General Properties ◽  
Finite Set ◽  
Numerical Tools ◽  
Loop Amplitudes

Abstract Scattering amplitudes in D dimensions involve particular terms that originate from the interplay of UV poles with the (D − 4)-dimensional parts of loop numerators. Such contributions can be controlled through a finite set of process-independent rational counterterms, which make it possible to compute loop amplitudes with numerical tools that construct the loop numerators in four dimensions. Building on a recent study [1] of the general properties of two-loop rational counterterms, in this paper we investigate their dependence on the choice of renormalisation scheme. We identify a nontrivial form of scheme dependence, which originates from the interplay of mass and field renormalisation with the (D−4)-dimensional parts of loop numerators, and we show that it can be controlled through a new kind of one-loop counterterms. This guarantees that the two-loop rational counterterms for a given renormalisable theory can be derived once and for all in terms of generic renormalisation constants, which can be adapted a posteriori to any scheme. Using this approach, we present the first calculation of the full set of two-loop rational counterterms in Yang-Mills theories. The results are applicable to SU(N) and U(1) gauge theories coupled to nf fermions with arbitrary masses.

scholarly journals ANTI-DE SITTER SPACE, THERMAL PHASE TRANSITION AND CONFINEMENT IN GAUGE THEORIES

2001 ◽  
Vol 16 (16) ◽  
pp. 2747-2769 ◽  
Author(s):  
EDWARD WITTEN
Keyword(s):  
Gauge Theories ◽  
De Sitter Space ◽  
Spontaneous Breaking ◽  
De Sitter ◽  
Four Dimensions ◽  
Yang Mills ◽  
Conformal Field ◽  
Classical Geometry ◽  
Large N ◽  
Quantum Phenomena

The correspondence between supergravity (and string theory) on AdS space and boundary conformal field theory relates the thermodynamics of [Formula: see text] super-Yang–Mills theory in four dimensions to the thermodynamics of Schwarzschild black holes in anti-de Sitter space. In this description, quantum phenomena such as the spontaneous breaking of the center of the gauge group, magnetic confinement and the mass gap are coded in classical geometry. The correspondence makes it manifest that the entropy of a very large AdS Schwarzschild black hole must scale "holographically" with the volume of its horizon. By similar methods, one can also make a speculative proposal for the description of large N gauge theories in four dimensions without supersymmetry.

scholarly journals Scattering amplitudes and the double copy in topologically massive theories

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Nathan Moynihan
Keyword(s):  
Gauge Theory ◽  
Scattering Amplitudes ◽  
Gauge Theories ◽  
Three Dimensional ◽  
Landau Gauge ◽  
Massive Gravity ◽  
Gauge Bosons ◽  
Four Dimensions ◽  
Recent Developments ◽  
Double Copy

Abstract Using the principles of the modern scattering amplitudes programme, we develop a formalism for constructing the amplitudes of three-dimensional topologically massive gauge theories and gravity. Inspired by recent developments in four dimensions, we construct the three-dimensional equivalent of x-variables, first defined in [1], for conserved matter currents coupled to topologically massive gauge bosons or gravitons. Using these, we bootstrap various matter-coupled gauge-theory and gravitational scattering amplitudes, and conjecture that topologically massive gauge theory and topologically massive gravity are related by the double copy. To motivate this idea further, we show explicitly that the Landau gauge propagator on the gauge theory side double copies to the de Donder gauge propagator on the gravity side.

scholarly journals DEFORMED SUPERSYMMETRIC GAUGE THEORIES FROM THE FLUXTRAP BACKGROUND

2013 ◽  
Vol 28 (28) ◽  
pp. 1330044 ◽  
Author(s):  
DOMENICO ORLANDO ◽  
SUSANNE REFFERT
Keyword(s):  
String Theory ◽  
Gauge Theories ◽  
Recent Literature ◽  
Supersymmetric Gauge Theories ◽  
Four Dimensions ◽  
Yang Mills ◽  
Supersymmetric Gauge ◽  
M Theory ◽  
Super Yang Mills Theory ◽  
Gravity Duals

The fluxtrap background of string theory provides a transparent and algorithmic way of constructing supersymmetric gauge theories with both mass and Ω-type deformations in various dimensions. In this paper, we review a number of deformed supersymmetric gauge theories in two and four dimensions which can be obtained via the fluxtrap background from string or M-theory. Such theories, the most well-known being Ω-deformed super-Yang–Mills theory in four dimensions, have met with a lot of interest in the recent literature. The string theory treatment offers many new avenues of analysis and applications, such as for example the study of the gravity duals for deformed [Formula: see text] gauge theories.

scholarly journals Quiver Gauge Theories: Finitude and Trichotomoty

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 291
Author(s):  
Yang-Hui He
Keyword(s):  
Gauge Theories ◽  
Beta Function ◽  
Asymptotic Freedom ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Four Dimensions ◽  
Yang Mills ◽  
Path Algebras ◽  
Representation Types ◽  
Standard Techniques

D-brane probes, Hanany-Witten setups and geometrical engineering stand as a trichotomy of standard techniques of constructing gauge theories from string theory. Meanwhile, asymptotic freedom, conformality and IR freedom pose as a trichotomy of the beta-function behaviour in quantum field theories. Parallel thereto is a trichotomy in set theory of finite, tame and wild representation types. At the intersection of the above lies the theory of quivers. We briefly review some of the terminology standard to the physics and to the mathematics. Then, we utilise certain results from graph theory and axiomatic representation theory of path algebras to address physical issues such as the implication of graph additivity to finiteness of gauge theories, the impossibility of constructing completely IR free string orbifold theories and the unclassifiability of N < 2 Yang-Mills theories in four dimensions.

scholarly journals Vector fields, RG flows and emergent gauge symmetry

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Daniel Nogradi
Keyword(s):  
Phase Diagram ◽  
Gauge Symmetry ◽  
Fixed Points ◽  
Vector Fields ◽  
Gauge Theories ◽  
The Other ◽  
Rich Phase ◽  
Four Dimensions ◽  
Yang Mills ◽  
Renormalizable Theory

Abstract We consider the most general perturbatively renormalizable theory of vector fields in four dimensions with a global SU(N) symmetry and massless couplings. The Lagrangian contains 1 quadratic, 2 cubic and 4 quartic couplings. The RG flow among this set of 7 couplings is computed to 1-loop and a rich phase diagram is mapped out; in particular it is shown that a finite number of asymptotically free RG-flows exist corresponding to non-trivial fixed points for the ratios of the couplings. None of these are gauge theories, i.e. possess only global SU(N) invariance but not a local one. We also include the most general ghost couplings, still with global SU(N) invariance, and compute the RG flow to 1-loop for all 9 resulting couplings. Again asymptotically free RG flows exist with non-trivial fixed points for the ratios of couplings. It is shown that Yang-Mills theory emerges at a particular fixed point. The theories at the other fixed points are marginally relevant gauge symmetry violating perturbations of Yang-Mills theory. The large-N limit is also investigated in detail.

SURPRISING SYMMETRY OF SCATTERING AMPLITUDES IN GAUGE THEORIES

2009 ◽  
Vol 24 (35n37) ◽  
pp. 2868-2881 ◽  
Author(s):  
G. P. KORCHEMSKY
Keyword(s):  
Scattering Amplitudes ◽  
String Duality ◽  
Recent Progress ◽  
Gauge Theories ◽  
Strongly Coupled ◽  
Superconformal Symmetry ◽  
Yang Mills ◽  
Arbitrary Coupling

I will review a recent progress in computing scattering amplitudes in strongly coupled gauge theories — a fascinating subject which has been recently boosted by the formulation of the gauge/string duality in maximally supersymmetric Yang–Mills theory. In addition to the conventional symmetry of the underlying Lagrangian, the scattering amplitudes in this theory exhibit a new, dual superconformal symmetry. This symmetry is powerful enough to completely determine the scattering amplitudes for arbitrary coupling in a suitably defined limit.

SURPRISING SYMMETRY OF SCATTERING AMPLITUDES IN GAUGE THEORIES

2010 ◽  
Vol 25 (02n03) ◽  
pp. 351-366
Author(s):  
G. P. KORCHEMSKY
Keyword(s):  
Scattering Amplitudes ◽  
String Duality ◽  
Recent Progress ◽  
Gauge Theories ◽  
Strongly Coupled ◽  
Superconformal Symmetry ◽  
Yang Mills ◽  
Arbitrary Coupling

I review a recent progress in computing scattering amplitudes in strongly coupled gauge theories - a fascinating subject which has been recently boosted by the formulation of the gauge/string duality in maximally supersymmetric Yang-Mills theory. In addition to the conventional symmetry of the underlying Lagrangian, the scattering amplitudes in this theory exhibit a new, dual superconformal symmetry. This symmetry is powerful enough to completely determine the scattering amplitudes for arbitrary coupling in a suitably defined limit.

scholarly journals Supersymmetry on the lattice

2016 ◽  
Vol 31 (22) ◽  
pp. 1643005 ◽  
Author(s):  
Georg Bergner ◽  
Simon Catterall
Keyword(s):  
Gauge Theories ◽  
Current Work ◽  
Four Dimensions ◽  
Yang Mills ◽  
Lattice Gauge ◽  
The Future ◽  
Lattice Gauge Theories

We discuss the motivations, difficulties and progress in the study of supersymmetric lattice gauge theories focusing in particular on [Formula: see text] and [Formula: see text] super-Yang–Mills in four dimensions. Brief reviews of the corresponding lattice formalisms are given and current results are presented and discussed. We conclude with a summary of the main aspects of current work and prospects for the future.

scholarly journals One-loop multicollinear limits from 2-point amplitudes on self-dual backgrounds

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Tim Adamo ◽  
Anton Ilderton ◽  
Alexander J. MacLeod
Keyword(s):  
Scattering Amplitudes ◽  
Plane Wave ◽  
Helicity Amplitude ◽  
Gauge Theories ◽  
Supersymmetric Gauge Theories ◽  
Yang Mills ◽  
Dual Plane ◽  
Supersymmetric Gauge ◽  
Background Fields ◽  
Plane Wave Background

Abstract For scattering amplitudes in strong background fields, it is — at least in principle — possible to perturbatively expand the background to obtain higher-point vacuum amplitudes. In the case of self-dual plane wave backgrounds we consider this expansion for two-point, one-loop amplitudes in pure Yang-Mills, QED and QCD. This enables us to obtain multicollinear limits of 1-loop vacuum amplitudes; the resulting helicity configurations are surprisingly restricted, with only the all-plus helicity amplitude surviving. These results are shown to be consistent with well-known vacuum amplitudes. We also show that for both abelian and non-abelian supersymmetric gauge theories, there is no helicity flip (and hence no vacuum birefringence) on any plane wave background, generalising a result previously known in the Euler-Heisenberg limit of super-QED.

scholarly journals Loop equation in Lattice gauge theories and bootstrap methods

2018 ◽  
Vol 175 ◽  
pp. 11011
Author(s):  
Peter Anderson ◽  
Martin Kruczenski
Keyword(s):  
Weak Coupling ◽  
Gauge Theories ◽  
Positive Definite Matrix ◽  
Mean Value ◽  
Four Dimensions ◽  
Yang Mills ◽  
Loop Equation ◽  
Lattice Gauge ◽  
The Mean ◽  
Lattice Gauge Theories

In principle the loop equation provides a complete formulation of a gauge theory purely in terms ofWilson loops. In the case of lattice gauge theories the loop equation is a well defined equation for a discrete set of quantities and can be easily solved at strong coupling either numerically or by series expansion. At weak coupling, however, we argue that the equations are not well defined unless a certain set of positivity constraints is imposed. Using semi-definite programming we show numerically that, for a pure Yang Mills theory in two, three and four dimensions, these constraints lead to good results for the mean value of the energy at weak coupling. Further, the positivity constraints imply the existence of a positive definite matrix whose entries are expectation values of Wilson loops. This matrix allows us to define a certain entropy associated with theWilson loops. We compute this entropy numerically and describe some of its properties. Finally we discuss some preliminary ideas for extending the results to supersymmetric N = 4 SYM.

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