scholarly journals Effective potential for SU(2) Polyakov loops and Wilson loop eigenvalues

2013 ◽  
Vol 88 (5) ◽  
Author(s):  
Dominik Smith ◽  
Adrian Dumitru ◽  
Robert Pisarski ◽  
Lorenz von Smekal
Keyword(s):  
Effective Potential ◽  
Wilson Loop ◽  
Polyakov Loops

TOPOLOGY OF THE GRASSMANNIAN σ MODEL ON A LATTICE

1987 ◽  
Vol 02 (08) ◽  
pp. 601-608 ◽  
Author(s):  
T. FUKAI ◽  
M. V. ATRE
Keyword(s):  
Partition Function ◽  
Strong Coupling ◽  
Wilson Loop ◽  
Strong Coupling Limit ◽  
Topological Term

The Grassmannian σ model with a topological term is studied on a lattice. The θ dependence of the partition function and the Wilson loop are evaluated in the strong coupling limit. The latter is shown to be independent of the area at θ = π, as in the CPN−1 model.

scholarly journals Gauge invariance, polar coordinates and inflation

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Ali Akil ◽  
Xi Tong
Keyword(s):  
Coordinate System ◽  
Effective Potential ◽  
Gauge Invariance ◽  
Polar Coordinates ◽  
Quantum Corrections ◽  
Background Current ◽  
Gauge Invariant ◽  
Gauge Dependence ◽  
Current Term ◽  
Invariant Current

Abstract We point out the necessity of resolving the apparent gauge dependence in the quantum corrections of cosmological observables for Higgs-like inflation models. We highlight the fact that this gauge dependence is due to the use of an asymmetric background current which is specific to a choice of coordinate system in the scalar manifold. Favoring simplicity over complexity, we further propose a practical shortcut to gauge-independent inflationary observables by using effective potential obtained from a polar-like background current choice. We demonstrate this shortcut for several explicit examples and present a gauge-independent prediction of inflationary observables in the Abelian Higgs model. Furthermore, with Nielsen’s gauge dependence identities, we show that for any theory to all orders, a gauge-invariant current term gives a gauge-independent effective potential and thus gauge-invariant inflationary observables.

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 Entanglement entropy for $$ \mathrm{T}\overline{\mathrm{T}} $$, $$ \mathrm{J}\overline{\mathrm{T}} $$, $$ \mathrm{T}\overline{\mathrm{J}} $$ deformed holographic CFT

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Soumangsu Chakraborty ◽  
Akikazu Hashimoto
Keyword(s):  
Parameter Space ◽  
Wilson Loop ◽  
Lorentz Invariance ◽  
Entanglement Entropy ◽  
Geodesic Equation ◽  
Leading Order ◽  
Theoretic Analysis ◽  
Expectation Value ◽  
Spatial Coordinates ◽  
Single Trace

Abstract We derive the geodesic equation for determining the Ryu-Takayanagi surface in AdS3 deformed by single trace $$ \mu T\overline{T} $$ μT T ¯ + $$ {\varepsilon}_{+}J\overline{T} $$ ε + J T ¯ + $$ {\varepsilon}_{-}T\overline{J} $$ ε − T J ¯ deformation for generic values of (μ, ε+, ε−) for which the background is free of singularities. For generic values of ε±, Lorentz invariance is broken, and the Ryu-Takayanagi surface embeds non-trivially in time as well as spatial coordinates. We solve the geodesic equation and characterize the UV and IR behavior of the entanglement entropy and the Casini-Huerta c-function. We comment on various features of these observables in the (μ, ε+, ε−) parameter space. We discuss the matching at leading order in small (μ, ε+, ε−) expansion of the entanglement entropy between the single trace deformed holographic system and a class of double trace deformed theories where a strictly field theoretic analysis is possible. We also comment on expectation value of a large rectangular Wilson loop-like observable.

scholarly journals Wilson loop algebras and quantum K-theory for Grassmannians

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Hans Jockers ◽  
Peter Mayr ◽  
Urmi Ninad ◽  
Alexander Tabler
Keyword(s):  
Wilson Loop ◽  
Gauge Theories ◽  
Wilson Line ◽  
Quantum Cohomology ◽  
Three Dimensional ◽  
Loop Algebra ◽  
Loop Algebras ◽  
Verlinde Algebra ◽  
K Theory ◽  
Chern Simons

Abstract We study the algebra of Wilson line operators in three-dimensional $$ \mathcal{N} $$ N = 2 supersymmetric U(M ) gauge theories with a Higgs phase related to a complex Grassmannian Gr(M, N ), and its connection to K-theoretic Gromov-Witten invariants for Gr(M, N ). For different Chern-Simons levels, the Wilson loop algebra realizes either the quantum cohomology of Gr(M, N ), isomorphic to the Verlinde algebra for U(M ), or the quantum K-theoretic ring of Schubert structure sheaves studied by mathematicians, or closely related algebras.

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