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 Massive Fluctuations in Deconfining SU(2) Yang-Mills Thermodynamics

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
Ingolf Bischer
Keyword(s):  
High Temperature ◽  
Quantitative Analysis ◽  
Ground State ◽  
Low Temperatures ◽  
Explicit Calculation ◽  
Loop Order ◽  
Loop Contribution ◽  
Yang Mills ◽  
Loop Expansion ◽  
Lower Loop

We review how vertex constraints inherited from the thermal ground state strongly reduce the integration support of loop four-momenta associated with massive quasiparticles in bubble diagrams constituting corrections to the free thermal quasiparticle pressure. In spite of the observed increasingly suppressing effect when increasing 2-particle-irreducible (2PI) loop order, a quantitative analysis enables us to disprove the conjecture voiced in hep-th/0609033 that the loop expansion would terminate at a finite order. This reveals the necessity to investigate exact expressions of (at least some) higher-loop order diagrams. Explicit calculation shows that although the behaviour of the 2PI three-loop contribution at low temperatures displays hierarchical suppression compared to lower loop orders, its high-temperature expression instead dominates all lower orders. However, an all-loop-order resummation of a class of 2PI bubble diagrams is shown to yield an analytic continuation of the low-temperature hierarchy to all temperatures in the deconfining phase.

scholarly journals SU(2) Yang-Mills thermodynamics: A priori estimate and radiative corrections

2018 ◽  
Vol 182 ◽  
pp. 02053 ◽  
Author(s):  
Ralf Hofmann
Keyword(s):  
Ground State ◽  
A Priori ◽  
Power Spectra ◽  
A Priori Estimate ◽  
Coarse Graining ◽  
Late Time ◽  
Radiative Corrections ◽  
Priori Estimate ◽  
Yang Mills ◽  
The One

We review and explain essential characteristics of the a priori estimate of the thermal ground state and its excitations in the deconfining phase of SU(2) Quantum Yang-Mills thermodynamics. This includes the spatially central and peripheral structure of Harrington-Shepard (anti)calorons, a sketch on how a spatial coarse-graining over (anti)caloron centers yields an inert scalar field, which is responsible for an adjoint Higgs mechanism, the identification of (anti)caloron action with ħ, a discussion of how, owing to (anti)caloron structure, the thermal ground state can be excited (wave-like and particlelike massless modes, massive thermal quasiparticle fluctuations), the principle role of and accounting for radiative corrections, the exclusion of energy-sign combinations due to constraints on momenta transfers in four-vertices in a completely fixed, physical gauge, dihedral diagrams and their resummation up to infinite loop order in the massive sector, and the resummation of the one-loop polarisation tensor of the massless modes. We also outline applications of deconfining SU(2) Yang-Mills thermodynamics to the Cosmic Microwave Background (CMB) which affect the cosmological model at high redshifts, the redshift for re-ionization of the Universe, the CMB angular power spectra at low l, and the late-time emergence of intergalactic magnetic fields.

SOME REMARKS CONCERNING THE FINITENESS OF N=4 SUPERSYMMETRIC YANG MILLS THEORIES

1988 ◽  
Vol 03 (01) ◽  
pp. 65-70 ◽  
Author(s):  
A. Bassetto ◽  
M. Dalbosco
Keyword(s):  
Light Cone ◽  
Green Functions ◽  
Loop Order ◽  
Light Cone Gauge ◽  
Yang Mills ◽  
Loop Level ◽  
Recent Treatment ◽  
The One

We carefully discuss the finiteness of SUSY YM N=4 in the light cone gauge, first at the one loop level by directly exhibiting the relevant terms of the lowest order Green functions and then at any loop order by using a recent treatment of the renormalization of general Yang-Mills theories in the light cone gauge. We point out the existence of a set of divergent Green functions which however do not contribute to observable quantities, thereby recovering consistency with formulations in other gauges.

scholarly journals RADIATIVE CORRECTIONS TO THE PRESSURE AND THE ONE-LOOP POLARIZATION TENSOR OF MASSLESS MODES IN SU(2) YANG–MILLS THERMODYNAMICS

2007 ◽  
Vol 22 (06) ◽  
pp. 1213-1237 ◽  
Author(s):  
MARKUS SCHWARZ ◽  
RALF HOFMANN ◽  
FRANCESCO GIACOSA
Keyword(s):  
Atomic Hydrogen ◽  
Black Body ◽  
Coulomb Gauge ◽  
Polarization Tensor ◽  
Radiative Corrections ◽  
Loop Correction ◽  
Yang Mills ◽  
Massless Mode ◽  
The Stability ◽  
The One

We compute the one-loop polarization tensor Π for the on-shell, massless mode in a thermalized SU(2) Yang–Mills theory being in its deconfining phase. Postulating that [Formula: see text], we discuss Π's effect on the low-momentum part of the black-body spectrum at temperatures ~2,…,4 T CMB where T CMB ~ 2.73 K . A table-top experiment is proposed to test the above postulate. As an application, we point out a possible connection with the stability of dilute, cold, and old innergalactic atomic hydrogen clouds. We also compute the two-loop correction to the pressure arising from the instantaneous massless mode in unitary-Coulomb gauge, which formerly was neglected, and present improved estimates for subdominant corrections.

Thermal Vacuum Polarization Using the Quantum Mechanical Path Integral

1997 ◽  
Vol 12 (30) ◽  
pp. 5387-5396 ◽  
Author(s):  
D. G. C. Mckeon
Keyword(s):  
Path Integral ◽  
Vacuum Polarization ◽  
Thermal Field ◽  
Quantum Mechanical ◽  
Loop Order ◽  
Thermal Vacuum ◽  
One Dimensional ◽  
Loop Expansion ◽  
High Temperature Expansion ◽  
The One

It has been shown how the quantum mechanical path integral can be used to do perturbative calculations in both quantum and thermal field theory to any order of the loop expansion. However, it is not readily apparent how gauge invariance is made manifest in this approach; in this paper we demonstrate how the vacuum polarization in electrodynamics at one-loop order is in fact transverse. We employ the one-dimensional Green's function [Formula: see text] in conjunction with an integration-by-parts procedure akin to that used by Strassler and Bern and Kosower. Surface terms in this approach are all zero. We obtain the high temperature expansion for the vacuum polarization in the static limit.

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.

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 ON THE POSSIBILITY OF CONSTRUCTING COVARIANT CHROMOMAGNETIC FIELD MODELS

1995 ◽  
Vol 10 (32) ◽  
pp. 2413-2425 ◽  
Author(s):  
ALEJANDRO CABO ◽  
SIANNAH PEÑARANDA ◽  
RENE MARTINEZ
Keyword(s):  
Perturbation Theory ◽  
Ground State ◽  
Mass Term ◽  
Spontaneous Generation ◽  
Polarization Tensor ◽  
Long Range Order ◽  
Loop Expansion ◽  
Gluon Condensates ◽  
Chromomagnetic Field ◽  
The One

Expressions for SO(4) invariant Euclidean QCD generating functionals are introduced which should produce nonvanishing gluon condensates. We consider first the loop expansion of the corresponding effectíve action searching for a description differing from the usual perturbation theory. At this level, we consider special free propagators which have off-diagonal long range order. The calculation of the polarization tensor leads to a gluon mass term which is proportional to the squared root of the finite value for <G2>. The summation of all the one-loop contributions to the energy having only mass insertions, indicates the spontaneous generation of the condensate from the perturbative ground state in a way resembling the similar effect in the case of chromomagnetic field models.

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