scholarly journals Wilson loops in 5d long quiver gauge theories

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Christoph F. Uhlemann
Keyword(s):  
Field Theory ◽  
Fixed Points ◽  
Wilson Loop ◽  
Gauge Theories ◽  
Internal Space ◽  
Wilson Loops ◽  
Expectation Values ◽  
Holographic Duals ◽  
Two Parameter ◽  
Supergravity Solution

Abstract Quiver gauge theories with a large number of nodes host a wealth of Wilson loop operators. Expectation values are obtained, using supersymmetric localization, for Wilson loops in the antisymmetric representations associated with each individual gauge node, for a sample of 5d long quiver gauge theories whose UV fixed points have holographic duals in Type IIB. The sample includes the TN theories and the results are uniformly given in terms of Bloch-Wigner functions. The holographic representation of the Wilson loops is identified. It comprises, for each supergravity solution, a two-parameter family of D3-branes which exactly reproduce the field theory results and identify points in the internal space with the faces of the associated 5-brane web. The expectation values of (anti)fundamental Wilson loops exhibit an enhanced scaling for many operators, which matches between field theory and supergravity.

scholarly journals BARYON MASSES AND WILSON LOOPS FOR FRACTIONAL D3-BRANE ON THE RESOLVED CONIFOLD

2002 ◽  
Vol 17 (28) ◽  
pp. 1871-1881
Author(s):  
SHIJONG RYANG
Keyword(s):  
Gauge Theory ◽  
Domain Wall ◽  
Wilson Loop ◽  
Wilson Loops ◽  
Baryon Mass ◽  
Area Law ◽  
Supergravity Solution

We study the ir dynamics of the type IIB supergravity solution describing N D3-branes and M fractional D3-branes on the resolved conifold. The baryon mass and the tension of domain wall in the dual gauge theory are evaluated and compared with those for the deformed conifold. The ir behavior of the solution for the general conifold is also discussed. We show that the area law behavior of the Wilson loop is attributed to the existence of the locus in the ir where the D3-brane charge vanishes.

scholarly journals The colored Jones polynomials as vortex partition functions

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Masahide Manabe ◽  
Seiji Terashima ◽  
Yuji Terashima
Keyword(s):  
Building Block ◽  
Wilson Loop ◽  
Gauge Theories ◽  
Partition Functions ◽  
Expectation Values ◽  
Abelian Gauge ◽  
Jones Polynomials ◽  
Knot Diagrams ◽  
Colored Jones Polynomials ◽  
Chern Simons

Abstract We construct 3D $$ \mathcal{N} $$ N = 2 abelian gauge theories on $$ \mathbbm{S} $$ S 2 × $$ \mathbbm{S} $$ S 1 labeled by knot diagrams whose K-theoretic vortex partition functions, each of which is a building block of twisted indices, give the colored Jones polynomials of knots in $$ \mathbbm{S} $$ S 3. The colored Jones polynomials are obtained as the Wilson loop expectation values along knots in SU(2) Chern-Simons gauge theories on $$ \mathbbm{S} $$ S 3, and then our construction provides an explicit correspondence between 3D $$ \mathcal{N} $$ N = 2 abelian gauge theories and 3D SU(2) Chern-Simons gauge theories. We verify, in particular, the applicability of our constructions to a class of tangle diagrams of 2-bridge knots with certain specific twists.

scholarly journals Wilson loop correlators in $$ \mathcal{N} $$ = 2 superconformal quivers

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Francesco Galvagno ◽  
Michelangelo Preti
Keyword(s):  
Wilson Loop ◽  
Vacuum Expectation ◽  
Wilson Loops ◽  
Expectation Values ◽  
Four Dimensions

Abstract We complete the program of [1] about perturbative approaches for $$ \mathcal{N} $$ N = 2 superconformal quiver theories in four dimensions. We consider several classes of observables in presence of Wilson loops, and we evaluate them with the help of supersymmetric localization. We compute Wilson loop vacuum expectation values, correlators of multiple coincident Wilson loops and one-point functions of chiral operators in presence of them acting as superconformal defects. We extend this analysis to the most general case considering chiral operators and multiple Wilson loops scattered in all the possible ways among the vector multiplets of the quiver. Finally, we identify twisted and untwisted observables which probe the orbifold of AdS5 × S5 with the aim of testing possible holographic perspectives of quiver theories in $$ \mathcal{N} $$ N = 2.

scholarly journals Localization and duality for ABJM latitude Wilson loops

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Luca Griguolo ◽  
Luigi Guerrini ◽  
Itamar Yaakov
Keyword(s):  
Quantum Mechanics ◽  
Wilson Loop ◽  
Gauge Theories ◽  
Bound State ◽  
Three Dimensions ◽  
Wilson Loops ◽  
Vortex Loop ◽  
Coulomb Branch ◽  
Vortex Loops ◽  
Chern Simons

Abstract We investigate several aspects of BPS latitude Wilson loops in gauge theories in three dimensions with $$ \mathcal{N} $$ N ≥ 4 supersymmetry. We derive a matrix model for the bosonic latitude Wilson loop in ABJM using supersymmetric localization, and show how to extend the computation to more general Chern-Simons-matter theories. We then define latitude type Wilson and vortex loop operators in theories without Chern-Simons terms, and explore a connection to the recently derived superalgebra defining local Higgs and Coulomb branch operators in these theories. Finally, we identify a BPS loop operator dual to the bosonic latitude Wilson loop which is a novel bound state of Wilson and vortex loops, defined using a worldvolume supersymmetric quantum mechanics.

scholarly journals Generalized global symmetries and holography

2018 ◽  
Vol 4 (1) ◽  
Author(s):  
Diego Hofman ◽  
Nabil Iqbal
Keyword(s):  
Field Theory ◽  
Global Symmetries ◽  
Gauge Theories ◽  
Gauge Fields ◽  
Goldstone Mode ◽  
Hydrodynamic Behavior ◽  
Conformal Field ◽  
Anisotropic Scaling ◽  
Holographic Duals ◽  
Chern Simons

We study the holographic duals of four-dimensional field theories with 1-form global symmetries, both discrete and continuous. Such higher-form global symmetries are associated with antisymmetric tensor gauge fields in the bulk. Various different realizations are possible: we demonstrate that a Maxwell action for the bulk antisymmetric gauge field results in a non-conformal field theory with a marginally running double-trace coupling. We explore its hydrodynamic behavior at finite temperature and make contact with recent symmetry-based formulations of magnetohydrodynamics. We also argue that discrete global symmetries on the boundary are dual to discrete gauge theories in the bulk. Such gauge theories have a bulk Chern-Simons description: we clarify the conventional 0-form case and work out the 1-form case. Depending on boundary conditions, such discrete symmetries may be embedded in continuous higher-form symmetries that are spontaneously broken. We study the resulting boundary Goldstone mode, which in the 1-form case may be thought of as a boundary photon. Our results clarify how the global form of the field theory gauge group is encoded in holography. Finally, we study the interplay of Maxwell and Chern-Simons terms put together. We work out the operator content and demonstrate the existence of new backreacted anisotropic scaling solutions that carry higher-form charge.

scholarly journals Wilson Loops in Antisymmetric Representations from Localization in Supersymmetric Gauge Theories

2018 ◽  
Vol 30 (07) ◽  
pp. 1840014
Author(s):  
Jorge G. Russo ◽  
Konstantin Zarembo
Keyword(s):  
Free Energy ◽  
Phase Transitions ◽  
Effective Mass ◽  
Wilson Loop ◽  
Gauge Theories ◽  
Wilson Loops ◽  
Two Phase ◽  
Fermi Distribution ◽  
Second Derivatives ◽  
Supersymmetric Gauge

Large-[Formula: see text] phase transitions occurring in massive [Formula: see text] theories can be probed by Wilson loops in large antisymmetric representations. The logarithm of the Wilson loop is effectively described by the free energy of a Fermi distribution and exhibits second-order phase transitions (discontinuities in the second derivatives) as the size of representation varies. We illustrate the general features of antisymmetric Wilson loops on a number of examples where the phase transitions are known to occur: [Formula: see text] SQCD with various mass arrangements and [Formula: see text] theory. As a byproduct, we solve planar [Formula: see text] SQCD with three independent mass parameters. This model has two effective mass scales and undergoes two phase transitions. In memory of Ludvig Dmitrievich Faddeev

PHASE HOLONOMY OF THE VACUUM IN THREE-DIMENSIONAL GAUGE THEORIES

1992 ◽  
Vol 07 (20) ◽  
pp. 4937-4948
Author(s):  
ROBERT LINK
Keyword(s):  
Field Theory ◽  
Gauge Field ◽  
Gauge Theories ◽  
Magnetic Monopole ◽  
Three Dimensional ◽  
Parameter Family ◽  
Two Parameter ◽  
Dirac Hamiltonian

The phase two-form of Berry in the neighborhood of a degeneracy of the Fock vacuum of a semisimple, nonabelian, second-quantized, relativistic fermion-background gauge field Hamiltonian is shown to be that of the Dirac magnetic monopole—thus extending a result of Berry to field theory. The Dirac Hamiltonian for an SU(2) fermion on the two-sphere is solved in a particular two-parameter family of background instanton gauge potentials as an explicit illustrative example.

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 Boundary conditions in topological AdS4/CFT3

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Pietro Benetti Genolini ◽  
Matan Grinberg ◽  
Paul Richmond
Keyword(s):  
Field Theory ◽  
Free Energy ◽  
Boundary Conditions ◽  
Smooth Solution ◽  
Three Dimensional ◽  
Field Theories ◽  
Legendre Transformation ◽  
Generating Functional ◽  
Holographic Duals

Abstract We revisit the construction in four-dimensional gauged Spin(4) supergravity of the holographic duals to topologically twisted three-dimensional $$ \mathcal{N} $$ N = 4 field theories. Our focus in this paper is to highlight some subtleties related to preserving supersymmetry in AdS/CFT, namely the inclusion of finite counterterms and the necessity of a Legendre transformation to find the dual to the field theory generating functional. Studying the geometry of these supergravity solutions, we conclude that the gravitational free energy is indeed independent from the metric of the boundary, and it vanishes for any smooth solution.

scholarly journals ABCD of ’t Hooft operators

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Hirotaka Hayashi ◽  
Takuya Okuda ◽  
Yutaka Yoshida
Keyword(s):  
Quantum Mechanics ◽  
Gauge Theories ◽  
Supersymmetric Quantum Mechanics ◽  
Type Ii ◽  
Expectation Values ◽  
String Theories

Abstract We compute by supersymmetric localization the expectation values of half-BPS ’t Hooft line operators in $$ \mathcal{N} $$ N = 2 U(N ), SO(N ) and USp(N ) gauge theories on S1 × ℝ3 with an Ω-deformation. We evaluate the non-perturbative contributions due to monopole screening by calculating the supersymmetric indices of the corresponding supersymmetric quantum mechanics, which we obtain by realizing the gauge theories and the ’t Hooft operators using branes and orientifolds in type II string theories.

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