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 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.

scholarly journals THE ζ FUNCTION ANSWER TO PARITY VIOLATION IN THREE-DIMENSIONAL GAUGE THEORIES

1996 ◽  
Vol 11 (15) ◽  
pp. 2643-2660 ◽  
Author(s):  
R.E. GAMBOA SARAVÍ ◽  
G.L. ROSSINI ◽  
F.A. SCHAPOSNIK
Keyword(s):  
Gauge Field ◽  
Parity Violation ◽  
Gauge Theories ◽  
Three Dimensional ◽  
Mass Term ◽  
Three Dimensions ◽  
Fermion Mass ◽  
Chern Simons ◽  
Fermion Current ◽  
Arbitrary Gauge

We study parity violation in (2+1)-dimensional gauge theories coupled to massive fermions. Using the ζ function regularization approach we evaluate the ground state fermion current in an arbitrary gauge field background, showing that it gets two different contributions which violate parity invariance and induce a Chern–Simons term in the gauge field effective action. One is related to the well-known classical parity breaking produced by a fermion mass term in three dimensions; the other, already present for massless fermions, is related to peculiarities of gauge-invariant regularization in odd-dimensional spaces.

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 Tests of Seiberg-like dualities in three dimensions

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Anton Kapustin ◽  
Brian Willett ◽  
Itamar Yaakov
Keyword(s):  
Gauge Theories ◽  
Three Dimensions ◽  
Simons Theory ◽  
Partition Functions ◽  
Seiberg Duality ◽  
Monopole Operators ◽  
Real Mass ◽  
Supersymmetric Gauge ◽  
The Relationship ◽  
Chern Simons

Abstract We use localization techniques to study several duality proposals for supersymmetric gauge theories in three dimensions reminiscent of Seiberg duality. We compare the partition functions of dual theories deformed by real mass terms and FI parameters. We find that Seiberg-like duality for $$ \mathcal{N} $$ N = 3 Chern-Simons gauge theories proposed by Giveon and Kutasov holds on the level of partition functions and is closely related to level-rank duality in pure Chern-Simons theory. We also clarify the relationship between the Giveon-Kutasov duality and a duality in theories of fractional M2 branes and propose a generalization of the latter. Our analysis also confirms previously known results concerning decoupled free sectors in $$ \mathcal{N} $$ N = 4 gauge theories realized by monopole operators.

scholarly journals Stochastic Loop Equations

1997 ◽  
Vol 12 (11) ◽  
pp. 2047-2059 ◽  
Author(s):  
D. V. Antonov
Keyword(s):  
Quantum Mechanics ◽  
Wilson Loop ◽  
Supersymmetric Quantum Mechanics ◽  
Wilson Loops ◽  
Stochastic Quantization ◽  
Suggested Approach ◽  
First Case ◽  
Loop Dynamics ◽  
Bilocal Field ◽  
Momentum Loop

Stochastic quantization is applied to derivation of the equations for the Wilson loops and generating functionals of the Wilson loops in the N = ∞ limit. These equations are treated both in the coordinate and momentum representations. In the first case the connection of the suggested approach with the problem of random closed contours and supersymmetric quantum mechanics is established, and the equation for the Quenched Master Field Wilson loop is derived. The regularized version of one of the obtained equations is presented and applied to derivation of the equation for the bilocal field correlator. The momentum loop dynamics is also investigated.

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 TOPOLOGICAL GAUGE THEORIES FROM SUPERSYMMETRIC QUANTUM MECHANICS ON SPACES OF CONNECTIONS

1993 ◽  
Vol 08 (03) ◽  
pp. 573-585 ◽  
Author(s):  
MATTHIAS BLAU ◽  
GEORGE THOMPSON
Keyword(s):  
Quantum Mechanics ◽  
Gauge Theory ◽  
Euler Characteristic ◽  
Moduli Spaces ◽  
Riemannian Geometry ◽  
Gauge Theories ◽  
Supersymmetric Quantum Mechanics ◽  
Three Dimensions ◽  
Flat Connections ◽  
Infinite Dimensional

We rederive the recently introduced N=2 topological gauge theories, representing the Euler characteristic of moduli spaces ℳ of connections, from supersymmetric quantum mechanics on the infinite-dimensional spaces [Formula: see text] of gauge orbits. To that end we discuss variants of ordinary supersymmetric quantum mechanics which have meaningful extensions to infinite-dimensional target spaces, and introduce supersymmetric quantum mechanics actions modeling the Riemannian geometry of submersions and embeddings, relevant to the projections [Formula: see text] and inclusions [Formula: see text] respectively. We explain the relation between Donaldson theory and the gauge theory of flat connections in three dimensions and illustrate the general construction by other two- and four-dimensional examples.

scholarly journals Witten effect, anomaly inflow, and charge teleportation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Hajime Fukuda ◽  
Kazuya Yonekura
Keyword(s):  
Quantum Mechanics ◽  
Magnetic Monopole ◽  
Charged Particles ◽  
Magnetic Monopoles ◽  
Three Dimensions ◽  
Total Charge ◽  
Four Dimensions ◽  
Linking Number ◽  
M Theory ◽  
Chern Simons

Abstract We study a phenomenon that electric charges are “teleported” between two spatially separated objects without exchanging charged particles at all. For example, this phenomenon happens between a magnetic monopole and an axion string in four dimensions, two vortices in three dimensions, and two M5-branes in M-theory in which M2-charges are teleported. This is realized by anomaly inflow into these objects in the presence of cubic Chern-Simons terms. In particular, the Witten effect on magnetic monopoles can be understood as a general consequence of anomaly inflow, which implies that some anomalous quantum mechanics must live on them. Charge violation occurs in the anomalous theories living on these objects, but it happens in such a way that the total charge is conserved between the two spatially separated objects. We derive a formula for the amount of the charge which is teleported between the two objects in terms of the linking number of their world volumes in spacetime.

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

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