Yang–Mills equations of motion for the Higgs sector of SU(3)-equivariant quiver gauge theories

We study the Yang-Mills theory and quantum gravity at finite temperature, in the presence of La-grange multiplier fields. These restrict the path integrals to field configurations which obey the classical equations of motion. This has the effect of doubling the usual one–loop thermal contributions and of suppressing all radiative corrections at higher loop order. Such theories are renormalizable at all temperatures. Some consequences of this result in quantum gravity are briefly examined.

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Geometry and Quantum Dynamics

10.1093/oso/9780198788393.003.0014 ◽

2017 ◽

Author(s):

Laurent Baulieu ◽

John Iliopoulos ◽

Roland Sénéor

Keyword(s):

General Relativity ◽

Quantum Dynamics ◽

Gauge Theories ◽

Brst Symmetry ◽

Abelian Gauge ◽

Yang Mills ◽

History Of ◽

Brst Invariance

A geometrical derivation of Abelian and non- Abelian gauge theories. The Faddeev–Popov quantisation. BRST invariance and ghost fields. General discussion of BRST symmetry. Application to Yang–Mills theories and general relativity. A brief history of gauge theories.

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Cohomological localization of $$ \mathcal{N} $$ = 2 gauge theories with matter

Journal of High Energy Physics ◽

10.1007/jhep09(2020)133 ◽

2020 ◽

Vol 2020 (9) ◽

Author(s):

Guido Festuccia ◽

Anastasios Gorantis ◽

Antonio Pittelli ◽

Konstantina Polydorou ◽

Lorenzo Ruggeri

Keyword(s):

Vector Field ◽

Extended Supersymmetry ◽

General Framework ◽

Gauge Theories ◽

Killing Vector ◽

Killing Vector Field ◽

Explicit Result ◽

Yang Mills ◽

Self Duality ◽

Witten Theory

Abstract We construct a large class of gauge theories with extended supersymmetry on four-dimensional manifolds with a Killing vector field and isolated fixed points. We extend previous results limited to super Yang-Mills theory to general $$ \mathcal{N} $$ N = 2 gauge theories including hypermultiplets. We present a general framework encompassing equivariant Donaldson-Witten theory and Pestun’s theory on S4 as two particular cases. This is achieved by expressing fields in cohomological variables, whose features are dictated by supersymmetry and require a generalized notion of self-duality for two-forms and of chirality for spinors. Finally, we implement localization techniques to compute the exact partition function of the cohomological theories we built up and write the explicit result for manifolds with diverse topologies.

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Two-loop rational terms in Yang-Mills theories

Journal of High Energy Physics ◽

10.1007/jhep10(2020)016 ◽

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.

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Local G2-manifolds, Higgs bundles and a colored quantum mechanics

Journal of High Energy Physics ◽

10.1007/jhep05(2021)002 ◽

2021 ◽

Vol 2021 (5) ◽

Author(s):

Max Hübner

Keyword(s):

Quantum Mechanics ◽

Gauge Theories ◽

Supersymmetric Quantum Mechanics ◽

Higgs Bundle ◽

Higgs Bundles ◽

View Point ◽

Yang Mills ◽

G2 Manifolds ◽

Supersymmetric Gauge ◽

M Theory

Abstract M-theory on local G2-manifolds engineers 4d minimally supersymmetric gauge theories. We consider ALE-fibered G2-manifolds and study the 4d physics from the view point of a partially twisted 7d supersymmetric Yang-Mills theory and its Higgs bundle. Euclidean M2-brane instantons descend to non-perturbative effects of the 7d supersymmetric Yang-Mills theory, which are found to be in one to one correspondence with the instantons of a colored supersymmetric quantum mechanics. We compute the contributions of M2-brane instantons to the 4d superpotential in the effective 7d description via localization in the colored quantum mechanics. Further we consider non-split Higgs bundles and analyze their 4d spectrum.

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On gauge independence for gauge models with soft breaking of BRST symmetry

International Journal of Modern Physics A ◽

10.1142/s0217751x1450184x ◽

2014 ◽

Vol 29 (30) ◽

pp. 1450184 ◽

Cited By ~ 10

Author(s):

Alexander Reshetnyak

Keyword(s):

Gauge Theories ◽

Brst Symmetry ◽

Landau Gauge ◽

Functional Integral ◽

Yang Mills ◽

Gauge Models ◽

S Matrix ◽

Gauge Fixing ◽

Dependent Parameter ◽

Quantum Treatment

A consistent quantum treatment of general gauge theories with an arbitrary gauge-fixing in the presence of soft breaking of the BRST symmetry in the field–antifield formalism is developed. It is based on a gauged (involving a field-dependent parameter) version of finite BRST transformations. The prescription allows one to restore the gauge-independence of the effective action at its extremals and therefore also that of the conventional S-matrix for a theory with BRST-breaking terms being additively introduced into a BRST-invariant action in order to achieve a consistency of the functional integral. We demonstrate the applicability of this prescription within the approach of functional renormalization group to the Yang–Mills and gravity theories. The Gribov–Zwanziger action and the refined Gribov–Zwanziger action for a many-parameter family of gauges, including the Coulomb, axial and covariant gauges, are derived perturbatively on the basis of finite gauged BRST transformations starting from Landau gauge. It is proved that gauge theories with soft breaking of BRST symmetry can be made consistent if the transformed BRST-breaking terms satisfy the same soft BRST symmetry breaking condition in the resulting gauge as the untransformed ones in the initial gauge, and also without this requirement.

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Higgsing towards E-strings

Journal of High Energy Physics ◽

10.1007/jhep01(2021)110 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Joonho Kim ◽

Seok Kim ◽

Kimyeong Lee

Keyword(s):

String Theory ◽

Gauge Theories ◽

The Self ◽

Flavor Symmetry ◽

Strongly Coupled ◽

Superconformal Field Theories ◽

Yang Mills ◽

Gauge Symmetries ◽

Elliptic Genera ◽

Linear Sigma Models

Abstract We explore 6d (1, 0) superconformal field theories with SU(3) and SU(2) gauge symmetries which cascade after Higgsing to the E-string theory on a single M5 near an E8 wall. Specifically, we study the 2d $$ \mathcal{N} $$ N = (0, 4) gauge theories which describe self-dual strings of these 6d theories. The self-dual strings can be also viewed as instanton string solitons of 6d Yang-Mills theories. We find the 2d anomaly-free gauge theories for self-dual strings, amending the naive ADHM gauge theories which are anomalous, and calculate their elliptic genera. While these 2d theories respect the flavor symmetry of each 6d SCFT only partially, their elliptic genera manifest the symmetry fully as these functions as BPS index are invariant in strongly coupled IR limit. Our consistent 2d (0, 4) gauge theories also provide new insights on the non-linear sigma models for the instanton strings, providing novel UV completions of the small instanton singularities. Finally, we construct new 2d quiver gauge theories for the self-dual strings in 6d E-string theory for multiple M5-branes probing the E8 wall, and find their fully refined elliptic genera.

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

International Journal of Modern Physics A ◽

10.1142/s0217751x01004451 ◽

2001 ◽

Vol 16 (16) ◽

pp. 2747-2769 ◽

Cited By ~ 6

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.

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