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 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 An E11 invariant gauge fixing

2018 ◽  
Vol 33 (01) ◽  
pp. 1850009 ◽  
Author(s):  
Michaella Pettit ◽  
Peter West
Keyword(s):  
Direct Product ◽  
Tangent Space ◽  
Space Time ◽  
Vector Representation ◽  
Alternative Derivation ◽  
Four Dimensions ◽  
Gauge Fixing ◽  
Cartan Involution ◽  
Low Levels ◽  
Invariant Gauge

We consider the nonlinear realisation of the semi-direct product of [Formula: see text] and its vector representation which leads to a space-time with tangent group that is the Cartan involution invariant subalgebra of [Formula: see text]. We give an alternative derivation of the invariant tangent space metric that this space–time possesses and compute this metric at low levels in eleven, five and four dimensions. We show that one can gauge fix the nonlinear realisation in an [Formula: see text] invariant manner.

scholarly journals AN EXACT RG FORMULATION OF QUANTUM GAUGE THEORY

2001 ◽  
Vol 16 (11) ◽  
pp. 1899-1911 ◽  
Author(s):  
T. R. MORRIS
Keyword(s):  
Gauge Theory ◽  
Flow Equation ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Quantum Gauge Theory ◽  
Supergauge Theory ◽  
Gauge Fixing ◽  
Β Function ◽  
The One ◽  
First Time

A gauge invariant Wilsonian effective action is constructed for pure SU(N) Yang-Mills theory by formulating the corresponding flow equation. Manifestly gauge invariant calculations can be performed i.e. without gauge fixing or ghosts. Regularisation is implemented in a novel way which realises a spontaneously broken SU(N|N) supergauge theory. As an example we sketch the computation of the one-loop β function, performed for the first time without any gauge fixing.

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.

The effect of renormalization in a finite massive theory

1995 ◽  
Vol 73 (9-10) ◽  
pp. 615-618
Author(s):  
D. G. C. McKeon
Keyword(s):  
Renormalization Group ◽  
Pole Mass ◽  
Coupling Constant ◽  
Loop Order ◽  
Effective Coupling ◽  
Yang Mills ◽  
Effective Coupling Constant ◽  
Group A ◽  
Massive Theory ◽  
Β Function

The fact that a theory is finite does not preclude the possibility of making finite renormalizations. With this in mind, we consider massive N = 4 super Yang–Mills theory, a model known to have a vanishing β function and to be finite at one-loop order when one uses the formulation using N = 1 superfields. The mass that appears in the Lagrangian is not a pole of the propagator when radiative effects are included; we fix the position of this pole and then discuss how the effective coupling constant in the theory depends on this pole mass. This procedure is akin to the original Gell-Mann–Low approach to the renormalization group. A one-loop calculation indicates that the effective coupling vanishes as the pole mass goes to zero and diverges for large values of the pole mass.

scholarly journals PERTURBATIVE ANALYSIS OF CHERN–SIMONS FIELD THEORY IN THE COULOMB GAUGE

1998 ◽  
Vol 13 (11) ◽  
pp. 1773-1783 ◽  
Author(s):  
FRANCO FERRARI ◽  
IGNAZIO LAZZIZZERA
Keyword(s):  
Perturbative Expansion ◽  
Coulomb Gauge ◽  
Feynman Diagrams ◽  
Field Theories ◽  
Green Functions ◽  
Loop Order ◽  
Yang Mills ◽  
Gauge Fixing ◽  
Infrared Divergences ◽  
Chern Simons

In this paper, we analyse the perturbative aspects of Chern–Simons field theories in the Coulomb gauge. We show that in the perturbative expansion of the Green functions there are neither ultraviolet nor infrared divergences. Moreover, all the radiative corrections are zero at any loop order. Some problems connected with the Coulomb gauge fixing, like the appearance of spurious singularities in the computation of the Feynman diagrams, are discussed and solved. The regularization used here for the spurious singularities can be easily applied also to the Yang–Mills case, which is affected by similar divergences.

The first-order formalism for Yang–Mills theory

1994 ◽  
Vol 72 (9-10) ◽  
pp. 601-607 ◽  
Author(s):  
D. G. C. McKeon
Keyword(s):  
Background Field ◽  
Loop Order ◽  
Point Function ◽  
Yang Mills ◽  
First Order ◽  
Order Form ◽  
Effective Lagrangian ◽  
Gauge Fixing ◽  
Vector Formula ◽  
Field Quantization

It is possible to replace the second-order Yang–Mills Lagrangian [Formula: see text] with the first-order Lagrangian [Formula: see text]. In this form, the interaction term in the Lagrangian, [Formula: see text] is very simple; the only disadvantage is that now not only the vector [Formula: see text] but also the auxiliary field [Formula: see text] propagate. The gauge-fixing and ghost contributions to the effective Lagrangian can similarly be reduced to first-order form by the introduction of auxiliary fields. We demonstrate the procedure by computing the two-point function to one-loop order using background field quantization.

scholarly journals The renormalization group with exact β-functions

2006 ◽  
Vol 84 (2) ◽  
pp. 131-143 ◽  
Author(s):  
V Elias ◽  
D.G.C. McKeon
Keyword(s):  
Background Field ◽  
Renormalization Scheme ◽  
Minimal Subtraction ◽  
Subtraction Scheme ◽  
Yang Mills ◽  
Minimal Subtraction Scheme ◽  
Text Model ◽  
Β Function ◽  
Supersymmetric Theories ◽  
The Relationship

The perturbative β-function is known exactly in a number of supersymmetric theories and in the ‘t Hooft renormalization scheme in the [Formula: see text] model. It is shown how this allows one to compute the effective action exactly for certain background field configurations and to relate bare and renormalized couplings. The relationship between the minimal subtraction scheme and the supersymmetry subtraction scheme in N = 1 super Yang–Mills theory is discussed.PACS No.: 11.10Z

Preregularization

1985 ◽  
Vol 63 (11) ◽  
pp. 1453-1465 ◽  
Author(s):  
V. Elias ◽  
R. B. Mann ◽  
A. M. Chowdhury ◽  
G. McKeon ◽  
S. Samant ◽  
...  
Keyword(s):  
Quantum Electrodynamics ◽  
Chiral Anomaly ◽  
Four Dimensions ◽  
Yang Mills ◽  
Integration Variable ◽  
Variable Surface ◽  
Feynman Amplitudes ◽  
Supersymmetric Theories ◽  
Super Yang Mills Theory

We describe and investigate the applicability of a recently proposed preregularization procedure in which arbitrary shift-of-integration-variable surface terms (in four dimensions) arising from loop-mementum ambiguities are constrained to absorb any contributions to unrenormalized Feynman amplitudes that violate Ward–Takahashi–Slavnov–Taylor (WTST) identities appropriate to the theory under consideration. Anomalies in WTST identities are shown to be the result of having insufficient arbitrariness in the loop momenta to accommodate the full set of Lagrangian symmetries. We demonstrate the utility of our procedure by analyzing the chiral anomaly in even dimensions, the supercurrent anomaly in N = 1 super Yang–Mills theory, and by calculations in quantum electrodynamics and Yang–Mills theory. We argue that the preregularization procedure should be particularly well suited to supersymmetric theories as a regularization-independent means of upholding super-WTST identities.

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