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 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 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 Evidence for weak-coupling holography from the gauge/gravity correspondence for Dp-branes

2020 ◽  
Vol 2020 (2) ◽  
Author(s):  
Yasuhiro Sekino
Keyword(s):  
Gauge Theory ◽  
Free Field ◽  
Scalar Fields ◽  
Superstring Theory ◽  
Spatial Direction ◽  
Strongly Coupled ◽  
Yang Mills ◽  
Hooft Coupling ◽  
Brane Solution ◽  
Gauge Gravity

Abstract Gauge/gravity correspondence is regarded as a powerful tool for the study of strongly coupled quantum systems, but its proof is not available. An unresolved issue that should be closely related to the proof is what kind of correspondence exists, if any, when gauge theory is weakly coupled. We report progress about this limit for the case associated with D$p$-branes ($0\le p\le 4$), namely, the duality between the $(p+1)$D maximally supersymmetric Yang–Mills theory and superstring theory on the near-horizon limit of the D$p$-brane solution. It has been suggested by supergravity analysis that the two-point functions of certain operators in gauge theory obey a power law with the power different from the free-field value for $p\neq 3$. In this work, we show for the first time that the free-field result can be reproduced by superstring theory on the strongly curved background. The operator that we consider is of the form ${\rm Tr}(Z^J)$, where $Z$ is a complex combination of two scalar fields. We assume that the corresponding string has the worldsheet spatial direction discretized into $J$ bits, and use the fact that these bits become non-interacting when ’t Hooft coupling is zero.

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.

D3/D5 SYSTEM AND HOLOGRAPHIC INTERFACE CFT

2013 ◽  
Vol 21 ◽  
pp. 159-160
Author(s):  
KOICHI NAGASAKI ◽  
SATOSHI YAMAGUCHI
Keyword(s):  
Gauge Theory ◽  
Potential Energy ◽  
Test Particle ◽  
Wilson Loop ◽  
Gauge Theories ◽  
The Other ◽  
Expectation Value ◽  
Fundamental String ◽  
Theory Result ◽  
Supersymmetric Gauge

We consider two [Formula: see text] supersymmetric gauge theories connected by an interface and the gravity dual of this system. This interface is expressed by a fuzzy funnel solution of Nahmfs equation in the gauge theory side. The gravity dual is a probe D5-brane in AdS5 × S5. The potential energy between this interface and a test particle is calculated in both the gauge theory side and the gravity side by the expectation value of a Wilson loop. In the gauge theory it is evaluated by just substituting the classical solution to the Wilson loop. On the other hand it is done by the on-shell action of the fundamental string stretched between the AdS boundary and the D5-brane in the gravity. We show the gauge theory result and the gravity one agree with each other.

scholarly journals Strong coupling expansion of free energy and BPS Wilson loop in $$ \mathcal{N} $$ = 2 superconformal models with fundamental hypermultiplets

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
M. Beccaria ◽  
G. V. Dunne ◽  
A. A. Tseytlin
Keyword(s):  
Free Energy ◽  
Strong Coupling ◽  
Wilson Loop ◽  
Strong Coupling Expansion ◽  
Gauge Groups ◽  
Hooft Coupling ◽  
Link Type ◽  
Rank 2 ◽  
Strong Coupling Expansions ◽  
Differential Relations

Abstract As a continuation of the study (in arXiv:2102.07696 and arXiv:2104.12625) of strong-coupling expansion of non-planar corrections in $$ \mathcal{N} $$ N = 2 4d superconformal models we consider two special theories with gauge groups SU(N) and Sp(2N). They contain N-independent numbers of hypermultiplets in rank 2 antisymmetric and fundamental representations and are planar-equivalent to the corresponding $$ \mathcal{N} $$ N = 4 SYM theories. These $$ \mathcal{N} $$ N = 2 theories can be realised on a system of N D3-branes with a finite number of D7-branes and O7-plane; the dual string theories should be particular orientifolds of AdS5 × S5 superstring. Starting with the localization matrix model representation for the $$ \mathcal{N} $$ N = 2 partition function on S4 we find exact differential relations between the 1/N terms in the corresponding free energy F and the $$ \frac{1}{2} $$ 1 2 -BPS Wilson loop expectation value $$ \left\langle \mathcal{W}\right\rangle $$ W and also compute their large ’t Hooft coupling (λ » 1) expansions. The structure of these expansions is different from the previously studied models without fundamental hypermultiplets. In the more tractable Sp(2N) case we find an exact resummed expression for the leading strong coupling terms at each order in the 1/N expansion. We also determine the exponentially suppressed at large λ contributions to the non-planar corrections to F and $$ \left\langle \mathcal{W}\right\rangle $$ W and comment on their resurgence properties. We discuss dual string theory interpretation of these strong coupling expansions.

scholarly journals ON THE CLASSICAL STRING SOLUTIONS AND STRING/FIELD THEORY DUALITY II

2004 ◽  
Vol 19 (26) ◽  
pp. 4475-4502 ◽  
Author(s):  
D. ALEKSANDROVA ◽  
P. BOZHILOV
Keyword(s):  
Field Theory ◽  
Black Hole ◽  
Gauge Theory ◽  
String Theory ◽  
String Field Theory ◽  
Semiclassical Limit ◽  
Hooft Coupling ◽  
Spatial Parameter ◽  
Black Hole Background

Based on the recently considered classical string configurations, in the framework of the semiclassical limit of the string/gauge theory correspondence, we describe a procedure for obtaining exact classical string solutions in general string theory backgrounds, when the string embedding coordinates depend nonlinearly on the worldsheet spatial parameter. The tensionless limit, corresponding to small 't Hooft coupling on the field theory side, is also considered. Applying the developed approach, we first reproduce some known results. Then, we find new string solutions — with two spins in AdS 5 black hole background and in AdS 5× S 5 with two spins and up to nine independent conserved R-charges.

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.

Sign in / Sign up

Export Citation Format

Share Document