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.

Aharony–Bergman–Jafferis–Maldacena Wilson Loops in the Fermi Gas Approach

2013 ◽  
Vol 68 (1-2) ◽  
pp. 178-209 ◽  
Author(s):  
Albrecht Klemm ◽  
Marcos Mariño ◽  
Masoud Soroush
Keyword(s):  
Vacuum Expectation ◽  
Fermi Gas ◽  
Wilson Loops ◽  
Winding Number ◽  
Airy Functions ◽  
Mechanical Problem ◽  
Expectation Values ◽  
The Matrix ◽  
Statistical Mechanical ◽  
Chern Simons

The matrix model of the Aharony-Bergman-Jafferis-Maldacena theory can be formulated in terms of an ideal Fermi gas with a non-trivial one-particle Hamiltonian. We show that, in this formalism, vacuum expectation values (vevs) of Wilson loops correspond to averages of operators in the statistical-mechanical problem. This makes it possible to calculate these vevs at all orders in 1/N, up to exponentially small corrections, and for arbitrary Chern-Simons coupling, by using the Wentzel- Kramer-Brillouin expansion.We present explicit results for the vevs of 1/6 and the 1/2 Bogomolnyi- Prasad-Sommerfield Wilson loops, at any winding number, in terms of Airy functions. Our expressions are shown to reproduce the low genus results obtained previously in the ’t Hooft expansion.

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 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 Quiver matrix model of ADHM type and BPS state counting in diverse dimensions

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Hiroaki Kanno
Keyword(s):  
Partition Function ◽  
Matrix Model ◽  
Characteristic Property ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Torus Action ◽  
Localization Theorem ◽  
Counting Problem ◽  
Expectation Value ◽  
Four Dimensions

Abstract We review the problem of Bogomol’nyi–Prasad–Sommerfield (BPS) state counting described by the generalized quiver matrix model of Atiyah–Drinfield–Hitchin–Manin type. In four dimensions the generating function of the counting gives the Nekrasov partition function, and we obtain a generalization in higher dimensions. By the localization theorem, the partition function is given by the sum of contributions from the fixed points of the torus action, which are labeled by partitions, plane partitions and solid partitions. The measure or the Boltzmann weight of the path integral can take the form of the plethystic exponential. Remarkably, after integration the partition function or the vacuum expectation value is again expressed in plethystic form. We regard it as a characteristic property of the BPS state counting problem, which is closely related to the integrability.

Vacuum expectation values of Higgs scalars in aSU(2)L×SU(2)R×U(1)gauge model

1979 ◽  
Vol 19 (5) ◽  
pp. 1601-1604
Author(s):  
T. Kitazoe ◽  
G. B. Mainland ◽  
K. Tanaka
Keyword(s):  
Vacuum Expectation ◽  
Gauge Model ◽  
Expectation Values

Gauge hierarchies for chiral SU(N) × SU(N) groups

1976 ◽  
Vol 54 (16) ◽  
pp. 1660-1663 ◽  
Author(s):  
Shalom Eliezer
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Gauge Theories ◽  
Vacuum Expectation ◽  
Coupling Constants ◽  
Spontaneous Breaking ◽  
Text Representation ◽  
Algebraic Equations ◽  
Expectation Values ◽  
Special Case

We have presented a special case where a hierarchy of spontaneous breaking of the symmetries can be achieved in conventional gauge theories (i.e. the Higgs scalars are elementary bosons and the coupling constants of the quartic interactions are small). We break spontaneously the chiral group SU(N) × SU(N) with Higgs scalars transforming like the (N, [Formula: see text]) representation of SU(N) × SU(N). By minimizing the potential we obtain a set of algebraic equations of the type[Formula: see text]where ηj are the vacuum expectation values of the Higgs scalars and μi2 and Aij are parameters. In order to get a hierarchy of spontaneous symmetry breaking we obtain the condition det Aij = 0.

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