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.

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.

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 BRST cohomology ofN= 2 super-Yang-Mills theory in four dimensions

2000 ◽  
Vol 26 (8) ◽  
pp. 1117-1130 ◽  
Author(s):  
A Tanzini ◽  
O S Ventura ◽  
L C Q Vilar ◽  
S P Sorella
Keyword(s):  
Four Dimensions ◽  
Yang Mills ◽  
Brst Cohomology ◽  
Super Yang Mills Theory

COSMOLOGICAL COMPACTIFICATION OF SUPERSTRINGS WITH DYNAMICAL DILATON FIELD IN FOUR DIMENSIONS

1992 ◽  
Vol 07 (39) ◽  
pp. 3647-3652 ◽  
Author(s):  
A.S. MAJUMDAR ◽  
A. MUKHERJEE ◽  
R.P. SAXENA
Keyword(s):  
Scale Factor ◽  
Dilaton Field ◽  
Four Dimensions ◽  
Yang Mills ◽  
Super Yang Mills Theory

The cosmological compactification of D=10, N=1 supergravity-super-Yang-Mills theory is studied. On requiring supersymmetry and the existence of a dynamical dilaton field in four dimensions, non-trivial evolution for the scale factor is obtained.

scholarly journals SL(3, ℤ) Modularity and New Cardy limits of the $$ \mathcal{N} $$ = 4 superconformal index

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Vishnu Jejjala ◽  
Yang Lei ◽  
Sam van Leuven ◽  
Wei Li
Keyword(s):  
Field Theory ◽  
Black Holes ◽  
Black Hole ◽  
Parameter Family ◽  
Similar Form ◽  
Four Dimensions ◽  
Yang Mills ◽  
Superconformal Index ◽  
Super Yang Mills Theory

Abstract The entropy of 1/16-th BPS AdS5 black holes can be microscopically accounted for by the superconformal index of the $$ \mathcal{N} $$ N = 4 super-Yang-Mills theory. One way to compute this is through a Cardy-like limit of a formula for the index obtained in [1] using the “S-transformation” of the elliptic Γ function. In this paper, we derive more general SL(3, ℤ) modular properties of the elliptic Γ function. We then use these properties to obtain a three integer parameter family of generalized Cardy-like limits of the $$ \mathcal{N} $$ N = 4 superconformal index. From these limits, we obtain entropy formulae that have a similar form as that of the original AdS5 black hole, up to an overall rescaling of the entropy. We interpret this both on the field theory and the gravitational side. Finally, we comment on how our work suggests a generalization of the Farey tail to four dimensions.

scholarly journals Super Yang-Mills theories with inhomogeneous mass deformations

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Yoonbai Kim ◽  
O-Kab Kwon ◽  
D. D. Tolla
Keyword(s):  
Boundary Condition ◽  
Killing Spinor ◽  
Vacuum Equation ◽  
Constant Mass ◽  
Yang Mills ◽  
Spatial Coordinate ◽  
Mass Functions ◽  
Vacuum Solutions ◽  
Super Yang Mills Theory

Abstract We construct the 4-dimensional $$ \mathcal{N}=\frac{1}{2} $$ N = 1 2 and $$ \mathcal{N} $$ N = 1 inhomogeneously mass-deformed super Yang-Mills theories from the $$ \mathcal{N} $$ N = 1* and $$ \mathcal{N} $$ N = 2* theories, respectively, and analyse their supersymmetric vacua. The inhomogeneity is attributed to the dependence of background fluxes in the type IIB supergravity on a single spatial coordinate. This gives rise to inhomogeneous mass functions in the $$ \mathcal{N} $$ N = 4 super Yang-Mills theory which describes the dynamics of D3-branes. The Killing spinor equations for those inhomogeneous theories lead to the supersymmetric vacuum equation and a boundary condition. We investigate two types of solutions in the $$ \mathcal{N}=\frac{1}{2} $$ N = 1 2 theory, corresponding to the cases of asymptotically constant mass functions and periodic mass functions. For the former case, the boundary condition gives a relation between the parameters of two possibly distinct vacua at the asymptotic boundaries. Brane interpretations for corresponding vacuum solutions in type IIB supergravity are also discussed. For the latter case, we obtain explicit forms of the periodic vacuum solutions.

scholarly journals Exact 1/N expansion of Wilson loop correlators in $$ \mathcal{N} $$ = 4 Super-Yang-Mills theory

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Wolfgang Mück
Keyword(s):  
Matrix Model ◽  
Wilson Loop ◽  
Model Solution ◽  
Wilson Loops ◽  
Combinatorial Formula ◽  
Expectation Value ◽  
Yang Mills ◽  
Hooft Coupling ◽  
The Matrix ◽  
Super Yang Mills Theory

Abstract Supersymmetric circular Wilson loops in $$ \mathcal{N} $$ N = 4 Super-Yang-Mills theory are discussed starting from their Gaussian matrix model representations. Previous results on the generating functions of Wilson loops are reviewed and extended to the more general case of two different loop contours, which is needed to discuss coincident loops with opposite orientations. A combinatorial formula representing the connected correlators of multiply wound Wilson loops in terms of the matrix model solution is derived. Two new results are obtained on the expectation value of the circular Wilson loop, the expansion of which into a series in 1/N and to all orders in the ’t Hooft coupling λ was derived by Drukker and Gross about twenty years ago. The connected correlators of two multiply wound Wilson loops with arbitrary winding numbers are calculated as a series in 1/N. The coefficient functions are derived not only as power series in λ, but also to all orders in λ by expressing them in terms of the coefficients of the Drukker and Gross series. This provides an efficient way to calculate the 1/N series, which can probably be generalized to higher-point correlators.

scholarly journals New bi-harmonic superspace formulation of 4D, $$ \mathcal{N} $$ = 4 SYM theory

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
I. L. Buchbinder ◽  
E. A. Ivanov ◽  
V. A. Ivanovskiy
Keyword(s):  
Effective Action ◽  
Harmonic Superspace ◽  
Four Dimensions ◽  
Yang Mills ◽  
Convenient Tool ◽  
Leading Term

Abstract We develop a novel bi-harmonic $$ \mathcal{N} $$ N = 4 superspace formulation of the $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory (SYM) in four dimensions. In this approach, the $$ \mathcal{N} $$ N = 4 SYM superfield constraints are solved in terms of on-shell $$ \mathcal{N} $$ N = 2 harmonic superfields. Such an approach provides a convenient tool of constructing the manifestly $$ \mathcal{N} $$ N = 4 supersymmetric invariants and further rewriting them in $$ \mathcal{N} $$ N = 2 harmonic superspace. In particular, we present $$ \mathcal{N} $$ N = 4 superfield form of the leading term in the $$ \mathcal{N} $$ N = 4 SYM effective action which was known previously in $$ \mathcal{N} $$ N = 2 superspace formulation.

scholarly journals Scrambling in Yang-Mills

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Robert de Mello Koch ◽  
Eunice Gandote ◽  
Augustine Larweh Mahu
Keyword(s):  
Relaxation Time ◽  
Weak Coupling ◽  
Degrees Of Freedom ◽  
Yang Mills ◽  
Hooft Coupling ◽  
Dilatation Operator ◽  
Super Yang Mills Theory

Abstract Acting on operators with a bare dimension ∆ ∼ N2 the dilatation operator of U(N) $$ \mathcal{N} $$ N = 4 super Yang-Mills theory defines a 2-local Hamiltonian acting on a graph. Degrees of freedom are associated with the vertices of the graph while edges correspond to terms in the Hamiltonian. The graph has p ∼ N vertices. Using this Hamiltonian, we study scrambling and equilibration in the large N Yang-Mills theory. We characterize the typical graph and thus the typical Hamiltonian. For the typical graph, the dynamics leads to scrambling in a time consistent with the fast scrambling conjecture. Further, the system exhibits a notion of equilibration with a relaxation time, at weak coupling, given by t ∼ $$ \frac{\rho }{\lambda } $$ ρ λ with λ the ’t Hooft coupling.

scholarly journals New modular invariants in $$ \mathcal{N} $$ = 4 Super-Yang-Mills theory

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Shai M. Chester ◽  
Michael B. Green ◽  
Silviu S. Pufu ◽  
Yifan Wang ◽  
Congkao Wen
Keyword(s):  
Eisenstein Series ◽  
Mass Parameter ◽  
Flat Space ◽  
Superstring Theory ◽  
Modular Invariant ◽  
Yang Mills ◽  
Laplace Eigenvalue ◽  
Modular Invariants ◽  
Tensor Multiplet ◽  
Super Yang Mills Theory

Abstract We study modular invariants arising in the four-point functions of the stress tensor multiplet operators of the $$ \mathcal{N} $$ N = 4 SU(N) super-Yang-Mills theory, in the limit where N is taken to be large while the complexified Yang-Mills coupling τ is held fixed. The specific four-point functions we consider are integrated correlators obtained by taking various combinations of four derivatives of the squashed sphere partition function of the $$ \mathcal{N} $$ N = 2∗ theory with respect to the squashing parameter b and mass parameter m, evaluated at the values b = 1 and m = 0 that correspond to the $$ \mathcal{N} $$ N = 4 theory on a round sphere. At each order in the 1/N expansion, these fourth derivatives are modular invariant functions of (τ,$$ \overline{\tau} $$ τ ¯ ). We present evidence that at half-integer orders in 1/N , these modular invariants are linear combinations of non-holomorphic Eisenstein series, while at integer orders in 1/N, they are certain “generalized Eisenstein series” which satisfy inhomogeneous Laplace eigenvalue equations on the hyperbolic plane. These results reproduce known features of the low-energy expansion of the four-graviton amplitude in type IIB superstring theory in ten-dimensional flat space and have interesting implications for the structure of the analogous expansion in AdS5× S5.

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