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

scholarly journals N = 1 SYM ACTION AND BRST COHOMOLOGY

2002 ◽  
Vol 17 (12) ◽  
pp. 739-749 ◽  
Author(s):  
K. ÜLKER
Keyword(s):  
Four Dimensions ◽  
Yang Mills ◽  
Brst Cohomology ◽  
Lower Dimensional ◽  
Exact Term

The relation between BRST cohomology and the N = 1 supersymmetric Yang–Mills action in four dimensions is discussed. In particular, it is shown that both off- and on-shell N = 1 SYM actions are related to a lower-dimensional field polynomial by solving the descent equations, which is obtained from the cohomological analysis of linearized Slavnov–Taylor operator ℬ, in the framework of algebraic renormalization. Furthermore we show that off- and on-shell solutions differ only by a ℬ-exact term, which is a consequence of the fact that the cohomology of both cases are the same.

scholarly journals N=2 SUPER-YANG–MILLS ACTION AND BRST COHOMOLOGY

2004 ◽  
Vol 19 (09) ◽  
pp. 713-726 ◽  
Author(s):  
K. ÜLKER
Keyword(s):  
Gauge Invariant ◽  
Yang Mills ◽  
Brst Cohomology ◽  
Lower Dimensional ◽  
Exact Term ◽  
Super Yang Mills Theory

The extended BRST cohomology of N=2 super-Yang–Mills theory is discussed in the framework of Algebraic Renormalization. In particular, N=2 supersymmetric descent equations are derived from the cohomological analysis of linearized Slavnov–Taylor operator ℬ. It is then shown that both off- and on-shell N=2 super-Yang–Mills actions are related to a lower-dimensional gauge-invariant field polynomial Tr ϕ2 by solving these descent equations. Moreover, it is found that these off- and on-shell solutions differ only by a ℬ-exact term, which can be interpreted as a consequence of the fact that the cohomology of both cases are the same.

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.

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.

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 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.

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