scholarly journals On three-point functions in ABJM and the latitude Wilson loop

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Marco S. Bianchi
Keyword(s):  
Gauge Group ◽  
Matrix Model ◽  
Wilson Loop ◽  
Weak Coupling ◽  
Structure Constant ◽  
Loop Order ◽  
Expectation Value ◽  
The Matrix

Abstract I consider three-point functions of twist-one operators in ABJM at weak coupling. I compute the structure constant of correlators involving one twist-one un-protected operator and two protected ones for a few finite values of the spin, up to two-loop order. As an application I enforce a limit on the gauge group ranks, in which I relate the structure constant for three chiral primary operators to the expectation value of a supersymmetric Wilson loop. Such a relation is then used to perform a successful five-loop test on the matrix model conjectured to describe the supersymmetric Wilson loop.

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 Wilson loops in $$ \mathcal{N} $$ = 4 SO(N) SYM and D-branes in AdS5 × ℝℙ5

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Simone Giombi ◽  
Bendeguz Offertaler
Keyword(s):  
String Theory ◽  
Gauge Group ◽  
Strong Coupling ◽  
Wilson Loop ◽  
Spinor Representation ◽  
Classical Action ◽  
Expectation Value ◽  
Yang Mills ◽  
Coupling Behavior ◽  
Type Iib String Theory

Abstract We study the half-BPS circular Wilson loop in $$ \mathcal{N} $$ N = 4 super Yang-Mills with orthogonal gauge group. By supersymmetric localization, its expectation value can be computed exactly from a matrix integral over the Lie algebra of SO(N). We focus on the large N limit and present some simple quantitative tests of the duality with type IIB string theory in AdS5× ℝℙ5. In particular, we show that the strong coupling limit of the expectation value of the Wilson loop in the spinor representation of the gauge group precisely matches the classical action of the dual string theory object, which is expected to be a D5-brane wrapping a ℝℙ4 subspace of ℝℙ5. We also briefly discuss the large N, large λ limits of the SO(N) Wilson loop in the symmetric/antisymmetric representations and their D3/D5-brane duals. Finally, we use the D5-brane description to extract the leading strong coupling behavior of the “bremsstrahlung function” associated to a spinor probe charge, or equivalently the normalization of the two-point function of the displacement operator on the spinor Wilson loop, and obtain agreement with the localization prediction.

scholarly journals BPS Wilson loop in $$ \mathcal{N} $$ = 2 superconformal SU(N) “orientifold” gauge theory and weak-strong coupling interpolation

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
M. Beccaria ◽  
G. V. Dunne ◽  
A. A. Tseytlin
Keyword(s):  
Gauge Theory ◽  
String Theory ◽  
Wilson Loop ◽  
Weak Coupling ◽  
Vector Multiplet ◽  
Superstring Theory ◽  
Expectation Value ◽  
Hooft Coupling ◽  
Rank 2 ◽  
Analytic Derivation

Abstract We consider the expectation value $$ \left\langle \mathcal{W}\right\rangle $$ W of the circular BPS Wilson loop in $$ \mathcal{N} $$ N = 2 superconformal SU(N) gauge theory containing a vector multiplet coupled to two hypermultiplets in rank-2 symmetric and antisymmetric representations. This theory admits a regular large N expansion, is planar-equivalent to $$ \mathcal{N} $$ N = 4 SYM theory and is expected to be dual to a certain orbifold/orientifold projection of AdS5× S5 superstring theory. On the string theory side $$ \left\langle \mathcal{W}\right\rangle $$ W is represented by the path integral expanded near the same AdS2 minimal surface as in the maximally supersymmetric case. Following the string theory argument in [5], we suggest that as in the $$ \mathcal{N} $$ N = 4 SYM case and in the $$ \mathcal{N} $$ N = 2 SU(N) × SU(N) superconformal quiver theory discussed in [19], the coefficient of the leading non-planar 1/N2 correction in $$ \left\langle \mathcal{W}\right\rangle $$ W should have the universal λ3/2 scaling at large ’t Hooft coupling. We confirm this prediction by starting with the localization matrix model representation for $$ \left\langle \mathcal{W}\right\rangle $$ W . We complement the analytic derivation of the λ3/2 scaling by a numerical high-precision resummation and extrapolation of the weak-coupling expansion using conformal mapping improved Padé analysis.

scholarly journals 1/N expansion of circular Wilson loop in $$ \mathcal{N} $$ = 2 superconformal SU(N) × SU(N) quiver

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
M. Beccaria ◽  
A.A. Tseytlin
Keyword(s):  
Free Energy ◽  
Gauge Theory ◽  
String Theory ◽  
Strong Coupling ◽  
Matrix Model ◽  
Wilson Loop ◽  
Numerical Study ◽  
Expectation Value ◽  
Non Gaussian ◽  
Localization Approach

Abstract Localization approach to $$ \mathcal{N} $$ N = 2 superconformal SU(N) × SU(N) quiver theory leads to a non-Gaussian two-matrix model representation for the expectation value of BPS circular SU(N) Wilson loop $$ \left\langle \mathcal{W}\right\rangle $$ W . We study the subleading 1/N2 term in the large N expansion of $$ \left\langle \mathcal{W}\right\rangle $$ W at weak and strong coupling. We concentrate on the case of the symmetric quiver with equal gauge couplings which is equivalent to the ℤ2 orbifold of the SU(2N) $$ \mathcal{N} $$ N = 4 SYM theory. This orbifold gauge theory should be dual to type IIB superstring in AdS5 × (S5/ℤ2). We present a string theory argument suggesting that the 1/N2 term in $$ \left\langle \mathcal{W}\right\rangle $$ W in the orbifold theory should have the same strong-coupling asymptotics λ3/2 as in the $$ \mathcal{N} $$ N = 4 SYM case. We support this prediction on the gauge theory side by a numerical study of the localization matrix model. We also find a relation between the 1/N2 term in the Wilson loop expectation value and the derivative of the free energy of the orbifold gauge theory on 4-sphere.

scholarly journals MATRIX MODEL FOR NONCOMMUTATIVE GRAVITY AND GRAVITATIONAL INSTANTONS

2004 ◽  
Vol 19 (02) ◽  
pp. 227-247 ◽  
Author(s):  
P. VALTANCOLI
Keyword(s):  
Gauge Group ◽  
Matrix Model ◽  
Equations Of Motion ◽  
Einstein Equations ◽  
Spin Connection ◽  
Metric Tensor ◽  
Gravitational Instantons ◽  
The Matrix ◽  
Noncommutative Gravity ◽  
Set Up

We introduce a matrix model for noncommutative gravity, based on the gauge group U (2)⊗ U (2). The vierbein is encoded in a matrix Yμ, having values in the coset space U (4)/( U (2)⊗ U (2)), while the spin connection is encoded in a matrix Xμ, having values in U (2)⊗ U (2). We show how to recover the Einstein equations from the θ→0 limit of the matrix model equations of motion. We stress the necessity of a metric tensor, which is a covariant representation of the gauge group in order to set up a consistent second order formalism. We finally define noncommutative gravitational instantons as generated by U (2)⊗ U (2) valued quasi-unitary operators acting on the background of the matrix model. Some of these solutions have naturally self-dual or anti-self-dual spin connections.

scholarly journals LOCALIZATION AND KNOTS

2013 ◽  
Vol 21 ◽  
pp. 195-196
Author(s):  
AKINORI TANAKA
Keyword(s):  
Gauge Group ◽  
Wilson Loop ◽  
Wilson Loops ◽  
Fundamental Representation ◽  
Localization Technique ◽  
Expectation Value ◽  
Three Sphere ◽  
Torus Knot

We study the 1/2 BPS condition of Wilson loop on squashed three-sphere, and find that the solution becomes torus knot or unknot. We also calculate the expectation value of 1/2 BPS Wilson loops by using localization technique with the gauge group U(2) and Wilson loop as fundamental representation. And it completely matches with known results.

scholarly journals Higher order RG flow on the Wilson line in $$ \mathcal{N} $$ = 4 SYM

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
M. Beccaria ◽  
S. Giombi ◽  
A. A. Tseytlin
Keyword(s):  
Wilson Loop ◽  
Weak Coupling ◽  
Anomalous Dimension ◽  
Wilson Line ◽  
Beta Function ◽  
Scalar Coupling ◽  
Model Approximation ◽  
Expectation Value ◽  
Hooft Coupling ◽  
Ladder Graphs

Abstract Extending earlier work, we find the two-loop term in the beta-function for the scalar coupling ζ in a generalized Wilson loop operator of the $$ \mathcal{N} $$ N = 4 SYM theory, working in the planar weak-coupling expansion. The beta-function for ζ has fixed points at ζ = ±1 and ζ = 0, corresponding respectively to the supersymmetric Wilson-Maldacena loop and to the standard Wilson loop without scalar coupling. As a consequence of our result for the beta-function, we obtain a prediction for the two-loop term in the anomalous dimension of the scalar field inserted on the standard Wilson loop. We also find a subset of higher-loop contributions (with highest powers of ζ at each order in ‘t Hooft coupling λ) coming from the scalar ladder graphs determining the corresponding terms in the five-loop beta-function. We discuss the related structure of the circular Wilson loop expectation value commenting, in particular, on consistency with a 1d defect version of the F-theorem. We also compute (to two loops in the planar ladder model approximation) the two-point correlators of scalars inserted on the Wilson line.

scholarly journals THE c=1 MATRIX MODEL FORMULATION OF TWO-DIMENSIONAL YANG-MILLS THEORIES

1993 ◽  
Vol 08 (33) ◽  
pp. 3201-3214 ◽  
Author(s):  
STEFANO PANZERI
Keyword(s):  
Gauge Group ◽  
Matrix Model ◽  
Model Description ◽  
Two Dimensional ◽  
Canonical Partition Function ◽  
Yang Mills ◽  
Grand Canonical Partition Function ◽  
Interesting Connection ◽  
The Matrix ◽  
Zero Coupling

We find the exact matrix model description of two-dimensional Yang-Mills theories on a cylinder or on a torus and with an arbitrary semisimple compact gauge group. This matrix model is the singlet sector of a c=1 matrix model where the matrix field is in the fundamental representation of the gauge group. We also prove that the basic constituents of the theory are Sutherland fermions in the zero coupling limit, and this leads to an interesting connection between two-dimensional gauge theories and one-dimensional integrable systems. In particular we derive for all the classical groups the exact grand canonical partition function of the free fermion system corresponding to a two-dimensional gauge theory on a torus.

scholarly journals The planar limit of $$ \mathcal{N} $$ = 2 superconformal quiver theories

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Bartomeu Fiol ◽  
Jairo Martfnez-Montoya ◽  
Alan Rios Fukelman
Keyword(s):  
Free Energy ◽  
Ising Model ◽  
Gauge Group ◽  
Wilson Loop ◽  
Cartan Matrix ◽  
Partition Functions ◽  
Expectation Value ◽  
Tree Graphs ◽  
Fundamental Matter ◽  
Planar Limit

Abstract We compute the planar limit of both the free energy and the expectation value of the 1/2 BPS wilson loop for four dimensional $$ \mathcal{N} $$ N = 2 superconformal quiver theories, with a product of SU(N)s as gauge group and hi-fundamental matter. Supersymmetric localization reduces the problem to a multi-matrix model, that we rewrite in the zero­ instanton sector as an effective action involving an infinite number of double-trace terms, determined by the relevant extended Cartan matrix. We find that the results, as in the case of $$ \mathcal{N} $$ N = 2 SCFTs with a simple gauge group, can be written as sums over tree graphs. For the $$ \hat{A_1} $$ A 1 ̂ case, we find that the contribution of each tree can be interpreted as the partition function of a generalized Ising model defined on the tree; we conjecture that the partition functions of these models defined on trees satisfy the Lee-Yang property, i.e. all their zeros lie on the unit circle.

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