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 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 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 On topological recursion for Wilson loops in $$ \mathcal{N} $$ = 4 SYM at strong coupling

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
M. Beccaria ◽  
A. Hasan
Keyword(s):  
Strong Coupling ◽  
Matrix Model ◽  
Wilson Loops ◽  
Expectation Value ◽  
Yang Mills ◽  
Usual Procedure ◽  
Topological Recursion ◽  
Sample Application ◽  
Single Trace ◽  
Genus Expansion

Abstract We consider U(N) $$ \mathcal{N} $$ N = 4 super Yang-Mills theory and discuss how to extract the strong coupling limit of non-planar corrections to observables involving the $$ \frac{1}{2} $$ 1 2 -BPS Wilson loop. Our approach is based on a suitable saddle point treatment of the Eynard-Orantin topological recursion in the Gaussian matrix model. Working directly at strong coupling we avoid the usual procedure of first computing observables at finite planar coupling λ, order by order in 1/N, and then taking the λ ≫ 1 limit. In the proposed approach, matrix model multi-point resolvents take a simplified form and some structures of the genus expansion, hardly visible at low order, may be identified and rigorously proved. As a sample application, we consider the expectation value of multiple coincident circular supersymmetric Wilson loops as well as their correlator with single trace chiral operators. For these quantities we provide novel results about the structure of their genus expansion at large tension, generalising recent results in arXiv:2011.02885.

FRACTAL WILSON LOOP IN U(1) LATTICE GAUGE THEORY

1993 ◽  
Vol 08 (05) ◽  
pp. 445-457
Author(s):  
H. KRÖGER ◽  
S. LANTAGNE ◽  
K.J.M. MORIARTY
Keyword(s):  
Gauge Theory ◽  
Strong Coupling ◽  
Wilson Loop ◽  
Lattice Gauge Theory ◽  
Strong Coupling Regime ◽  
Lattice Gauge ◽  
Area Law

Recently, a fractal Wilson loop <FP> has been suggested to yield for non-compact SU(2) gauge theory an area law in the strong-coupling regime, while the standard Wilson loop <WP> yields a perimeter law. Here we consider non-compact U(1) gauge theory, compute the fractal Wilson loop analytically, and obtain a perimeter law for all coupling. We find that <FP> and <WP> coincide.

scholarly journals ϵ-CORRECTED SEIBERG–WITTEN PREPOTENTIAL OBTAINED FROM HALF-GENUS EXPANSION IN β-DEFORMED MATRIX MODEL

2011 ◽  
Vol 26 (20) ◽  
pp. 3439-3467 ◽  
Author(s):  
H. ITOYAMA ◽  
N. YONEZAWA
Keyword(s):  
Free Energy ◽  
Supersymmetric Gauge Theory ◽  
Gauge Theory ◽  
Partition Function ◽  
Matrix Model ◽  
Conformal Block ◽  
Supersymmetric Gauge ◽  
Genus Expansion ◽  
Resolvent Function ◽  
Explicit Expressions

We consider the half-genus expansion of the resolvent function in the β-deformed matrix model with three-Penner potential under the AGT conjecture and the 0d–4d dictionary. The partition function of the model, after the specification of the paths, becomes the DF conformal block for fixed c and provides the Nekrasov partition function expanded both in [Formula: see text] and in ϵ = ϵ1+ϵ2. Exploiting the explicit expressions for the lower terms of the free energy extracted from the above expansion, we derive the first few ϵ corrections to the Seiberg–Witten prepotential in terms of the parameters of SU(2), Nf = 4, [Formula: see text] supersymmetric gauge theory.

THE STRING DIFFERENCE EQUATION OF THE D=1 MATRIX MODEL AND W1+∞ SYMMETRY OF THE KP HIERARCHY

1992 ◽  
Vol 07 (20) ◽  
pp. 4791-4802 ◽  
Author(s):  
M.A. AWADA ◽  
S.J. SIN
Keyword(s):  
Free Energy ◽  
String Theory ◽  
Difference Equation ◽  
Matrix Model ◽  
Zero Mode ◽  
Legendre Transformation ◽  
Kp Hierarchy ◽  
Kdv Hierarchy ◽  
The Difference ◽  
Special Case

We give a connection between the D=1 matrix model and the generalized KP hierarchy. First, we find a difference equation satisfied by F, the Legendre transformation of the free energy of the D=1 matrix model on a circle of radius R. Then we show that it is a special case of the difference equation of the generalized KP hierarchy with its zero mode identified with the scaling variable of the D=1 string theory. We propose that the massive D=1 matrix model is described by the generalized KP hierarchy, which implies the manifest integrability of D=1 string theory. We also show that the (generalized) KP hierarchy has an underlying W1+∞ symmetry. By reduction, we prove that the generalized KdV hierarchy has a subalgebra of the above symmetry which again forms a W1+∞. We argue that there are no W constraints in D=1 string theory, which is in contrast to D<1 theories, where there are W1+∞ constraints.

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.

Sign in / Sign up

Export Citation Format

Share Document