scholarly journals Thermal Gauge Theories with Lagrange Multiplier Fields

2021 ◽  
Author(s):  
F.T. Brandt ◽  
J. Frenkel ◽  
S. Martins-Filho ◽  
G.S.S Sakoda ◽  
D.G.C. McKeon
Keyword(s):  
Quantum Gravity ◽  
Lagrange Multiplier ◽  
Finite Temperature ◽  
Gauge Theories ◽  
Equations Of Motion ◽  
Path Integrals ◽  
Radiative Corrections ◽  
Loop Order ◽  
Yang Mills

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.

scholarly journals A massive non-abelian vector model

2013 ◽  
Vol 91 (2) ◽  
pp. 164-167 ◽  
Author(s):  
F.A. Chishtie ◽  
D.G.C. McKeon
Keyword(s):  
Lagrange Multiplier ◽  
Equations Of Motion ◽  
Vector Model ◽  
Radiative Corrections

The introduction of a Lagrange multiplier field to ensure that the classical equations of motion are satisfied serves to restrict radiative corrections in a model to only one loop. The consequences of this for a massive non-abelian vector model are considered.

scholarly journals Massive loops in thermal SU(2) Yang–Mills theory: Radiative corrections to the pressure beyond two loops

2017 ◽  
Vol 32 (19n20) ◽  
pp. 1750118 ◽  
Author(s):  
Ingolf Bischer ◽  
Thierry Grandou ◽  
Ralf Hofmann
Keyword(s):  
Low Temperature ◽  
Ground State ◽  
Analytical Continuation ◽  
Radiative Corrections ◽  
Loop Order ◽  
Strong Suppression ◽  
Yang Mills ◽  
Loop Expansion ◽  
The One ◽  
Lower Loop

We address the loop expansion of the pressure in the deconfining phase of SU(2) Yang–Mills thermodynamics. We devise an efficient book-keeping of excluded energy-sign and scattering-channel combinations for the loop four-momenta associated with massive quasiparticles, circulating in (connected) bubble diagrams subject to vertex constraints inherited from the thermal ground state. These radiative corrections modify the one-loop pressure exerted by free thermal quasiparticles. Increasing the loop order in two-particle irreducible (2PI) bubble diagrams, we exemplarily demonstrate a suppressing effect of the vertex constraints on the number of valid combinations. This increasingly strong suppression gave rise to the conjecture in arXiv:hep-th/0609033 that the loop expansion would terminate at a finite order. Albeit the low-temperature dependence of the 2PI 3-loop diagram complies with this behavior, a thorough analysis of the high-temperature situation reveals that the leading power in temperature is thirteen such that this diagram dominates all lower loop orders for sufficiently high temperatures. An all-loop-order resummation of 2PI diagrams with dihedral symmetry is thus required, defining an extremely well-bounded analytical continuation of the low-temperature result.

scholarly journals Undoing decomposition

2019 ◽  
Vol 34 (35) ◽  
pp. 1950233 ◽  
Author(s):  
Eric Sharpe
Keyword(s):  
Sigma Model ◽  
Gauge Theories ◽  
Disjoint Union ◽  
Path Integrals ◽  
Two Dimensions ◽  
Linear Sigma Model ◽  
Two Dimensional ◽  
Yang Mills ◽  
Witten Theory ◽  
Supersymmetric Gauge

In this paper we discuss gauging one-form symmetries in two-dimensional theories. The existence of a global one-form symmetry in two dimensions typically signals a violation of cluster decomposition — an issue resolved by the observation that such theories decompose into disjoint unions, a result that has been applied to, for example, Gromov–Witten theory and gauged linear sigma model phases. In this paper we describe how gauging one-form symmetries in two-dimensional theories can be used to select particular elements of that disjoint union, effectively undoing decomposition. We examine such gaugings explicitly in examples involving orbifolds, nonsupersymmetric pure Yang–Mills theories, and supersymmetric gauge theories in two dimensions. Along the way, we learn explicit concrete details of the topological configurations that path integrals sum over when gauging a one-form symmetry, and we also uncover “hidden” one-form symmetries.

scholarly journals Yang–Mills mass gap at large-N, noncommutative YM theory, topological quantum field theory and hyperfiniteness

2015 ◽  
Vol 24 (06) ◽  
pp. 1530017 ◽  
Author(s):  
Marco Bochicchio
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Quantum Gravity ◽  
Gauge Theories ◽  
Floer Homology ◽  
Asymptotic Freedom ◽  
General Interest ◽  
Yang Mills ◽  
Mass Gap ◽  
Large N

We review a number of old and new concepts in quantum gauge theories, some of which are well-established but not widely appreciated, some are most recent, that may have analogs in gauge formulations of quantum gravity, loop quantum gravity, and their topological versions, and may be of general interest. Such concepts involve noncommutative gauge theories and their relation to the large-N limit, loop equations and the change to the anti-selfdual (ASD) variables also known as Nicolai map, topological field theory (TFT) and its relation to localization and Morse–Smale–Floer homology, with an emphasis both on the mathematical aspects and the physical meaning. These concepts, assembled in a new way, enter a line of attack to the problem of the mass gap in large-NSU(N) Yang–Mills (YM), that is reviewed as well. Algebraic considerations furnish a measure of the mathematical complexity of a complete solution of large-NSU(N) YM: In the large-N limit of pure SU(N) YM the ambient algebra of Wilson loops is known to be a type II1 nonhyperfinite factor. Nevertheless, for the mass gap problem at the leading 1/N order, only the subalgebra of local gauge-invariant single-trace operators matters. The connected two-point correlators in this subalgebra must be an infinite sum of propagators of free massive fields, since the interaction is subleading in [Formula: see text], a vast simplification. It is an open problem, determined by the growth of the degeneracy of the spectrum, whether the aforementioned local subalgebra is in fact hyperfinite. Moreover, the sum of free propagators that occurs in the two-point correlators in the aforementioned local subalgebra must be asymptotic for large momentum to the result implied by the asymptotic freedom and the renormalization group: This fundamental constraint fixes asymptotically the residues of the poles of the propagators in terms of the mass spectrum and of the anomalous dimensions of the local operators. For the mass gap problem, in the search of a hyperfinite subalgebra containing the scalar sector of large-N YM, a major role is played by the existence of a TFT underlying the large-N limit of YM, with twisted boundary conditions on a torus or, which is the same by Morita duality, on a noncommutative torus. The TFT is trivial at the leading large-N order and localized on a set of critical points by means of a quantum version of Morse–Smale–Floer homology, that involves loop equations in the ASD variables. A hyperfinite sector arises by fluctuations around the trivial TFT, in which the joint spectrum of scalar and pseudoscalar glueballs is linear in the square of the masses [Formula: see text] with degeneracy k = 1, 2,…, and the two-point correlator satisfies the aforementioned fundamental constraint arising by the asymptotic freedom and the renormalization group.

One-loop effects in N = 4 supersymmetry

1996 ◽  
Vol 74 (3-4) ◽  
pp. 176-181
Author(s):  
D. G. C. McKeon
Keyword(s):  
Radiative Corrections ◽  
Loop Order ◽  
Four Dimensions ◽  
Yang Mills ◽  
Yukawa Couplings ◽  
Gauge Fixing ◽  
Component Field ◽  
Β Function ◽  
Supersymmetric Theories ◽  
Invariant Gauge

It has been demonstrated that in massless supersymmetric theories, finite radiative corrections to the superpotential can occur (viz. the nonrenormalization theorems can be circumvented). In this paper, we examine the consequences of this in N = 4 supersymmetric Yang–Mills theory, a model in which the β function is known to be zero. It is shown that radiative corrections to the superpotential arise at one loop order in this theory contrary to the expectations of the nonrenormalization theorem, but that their form depends on which formulation of the model is used. When one uses a superfield formulation involving an N = 1 vector superfield and three N = 1 chiral superfields in conjunction with a supersymmetric (but not SU(4)) invariant gauge fixing, then at one-loop order, the radiative generation of terms in the superpotential means that the equality of the gauge and Yukawa couplings and indeed of different Yukawa couplings is lost. If one uses the component field formulation of the N = 4 model in the Wess–Zumino gauge with a covariant, SU(4) invariant (but not supersymmetric invariant) gauge fixing, then the SU(4) invariance is maintained, but the gauge and Yukawa couplings are no longer equal. We also consider computations in the component field formulation in the Wess–Zumino gauge using an N = 1 super Yang–Mills theory in ten dimensions, dimensionally reduced to four dimensions, with a ten-dimensional covariant gauge fixing condition. This formulation ensures that there is no distinction between gauge and Yukawa couplings and that SU(4) invariance is automatically preserved; however, supersymmetry is broken by the gauge fixing procedure.

A solvable four-dimensional model with gauge symmetry

1992 ◽  
Vol 70 (6) ◽  
pp. 441-450 ◽  
Author(s):  
D. G. C. McKeon ◽  
T. N. Sherry
Keyword(s):  
Vector Field ◽  
Lagrange Multiplier ◽  
Path Integral ◽  
Equations Of Motion ◽  
Background Field ◽  
Dynamical Theory ◽  
Vector Model ◽  
Quantum Field Theories ◽  
Yang Mills ◽  
Classical Lagrangian

Recently, interest has been focused on quantum field theories in which a Lagrange multiplier field occurs in the classical Lagrangian. This has the effect of restricting the sum over classical paths in the path integral to solutions of the classical field equation. Examples of such theories are the dynamical theory of two-dimensional gravity proposed by Jackiw and Teitelboim, the Chern–Simons formulation of gravity in 2 + 1 dimensions by Witten, and the path-integral formulation of classical systems by Gozzi. We examine, in this paper, a gauge theory in which a vector field [Formula: see text] acts as a Lagrange multiplier in the classical Lagrangian, ensuring that a vector field [Formula: see text] satisfies the Yang–Mills equations of motion. Quantization can be carried out either using BRST quantization or by using the Faddeev–Popov procedure. Either by explicitly integrating over the field [Formula: see text] and its associated ghost fields, or by directly examining the Feynman perturbation theory, it can be established that all diagrams beyond one-loop order vanish, allowing one to compute the one-particle irreducible generating functional exactly. Background-field quantization is introduced to simplify the renormalization program. The β function is computed in closed form. In an appendix we show how our interaction can be derived from Yang–Mills theory based on a group G or by considering the Yang–Mills theory for a group IG. This can be extended to deal with four interacting gauge fields. A second appendix deals with a scalar model that superficially resembles our vector model.

scholarly journals In-Medium Effects in the Holographic Quark-Gluon Plasma

2010 ◽  
Vol 2010 ◽  
pp. 1-141 ◽  
Author(s):  
Felix Rust
Keyword(s):  
Quark Gluon Plasma ◽  
Finite Temperature ◽  
Gauge Theories ◽  
Particle Density ◽  
Gluon Plasma ◽  
Strongly Coupled ◽  
Yang Mills ◽  
Fundamental Matter ◽  
Gauge Gravity ◽  
Gravity Duality

We use the gauge/gravity duality to investigate various properties of strongly coupled gauge theories, which we interpret as models for the quark-gluon plasma (QGP). In particular, we use variants of the D3/D7 setup as an implementation of the top-down approach of connecting string theory with phenomenologically relevant gauge theories. We focus on the effects of finite temperature and finite density on fundamental matter in the holographic quark-gluon plasma, which we model as theN=2hypermultiplet in addition to theN=4gauge multiplet of supersymmetric Yang-Mills theory. We use a setup in which we can describe the holographic plasma at finite temperature and either baryon or isospin density and investigate the properties of the system from three different viewpoints. (i) We study meson spectra. Our observations at finite temperature and particle density are in qualitative agreement with phenomenological models and experimental observations. They agree with previous publications in the according limits. (ii) We study the temperature and density dependence of transport properties of fundamental matter in the QGP. In particular, we obtain diffusion coefficients. Furthermore, in a kinetic model we estimate the effects of the coupling strength on meson diffusion and therewith equilibration processes in the QGP. (iii) We observe the effects of finite temperature and density on the phase structure of fundamental matter in the holographic QGP. We trace out the phase transition lines of different phases in the phase diagram.

scholarly journals Volume independence for Yang–Mills fields on the twisted torus

2014 ◽  
Vol 29 (25) ◽  
pp. 1445001 ◽  
Author(s):  
Margarita García Pérez ◽  
Antonio González-Arroyo ◽  
Masanori Okawa
Keyword(s):  
Perturbation Theory ◽  
Boundary Conditions ◽  
Gauge Theories ◽  
Field Theories ◽  
Gauge Fields ◽  
Dimensional Torus ◽  
Loop Order ◽  
Yang Mills ◽  
Hooft Coupling ◽  
Twisted Boundary Conditions

We review some recent results related to the notion of volume independence in SU (N) Yang–Mills theories. The topic is discussed in the context of gauge theories living on a d-dimensional torus with twisted boundary conditions. After a brief introduction reviewing the formalism for introducing gauge fields on a torus, we discuss how volume independence arises in perturbation theory. We show how, for appropriately chosen twist tensors, perturbative results to all orders in the 't Hooft coupling depend on a specific combination of the rank of the gauge group (N) and the periods of the torus (l), given by lN2/d, for d even. We discuss the well-known relation to noncommutative field theories and address certain threats to volume independence associated to the occurrence of tachyonic instabilities at one-loop order. We end by presenting some numerical results in 2+1 dimensions that extend these ideas to the nonperturbative domain.

Geometry and Quantum Dynamics

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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