BPS wilson loops in generic conformal $$ \mathcal{N} $$ = 2 SU(N) SYM theories

Conformal theories with a global symmetry may be studied in the double scaling regime where the interaction strength is reduced while the global charge increases. Here, we study generic 4d N = 2 SU (N ) gauge theories with conformal matter content at large R-charge Q R → ∞ with fixed 't Hooft-like coupling κ = Q R g 2 YM . Our analysis concerns two distinct classes of natural scaling functions. The first is built in terms of chiral/anti-chiral two-point functions. The second involves one-point functions of chiral operators in presence of 1 2 -BPS Wilson-Maldacena loops. In the rank-1 SU (2) case, the two-point sector has been recently shown to be captured by an auxiliary chiral random matrix model. We extend the analysis to SU (N ) theories and provide an algorithm that computes arbitrarily long perturbative expansions for all considered models, parametric in the rank. The leading and next-to-leading contributions are cross-checked by a three-loops computation in N = 1 superspace. This perturbative analysis identifies maximally non-planar Feynman diagrams as the relevant ones in the double scaling limit. In the Wilson-Maldacena sector, we obtain closed expressions for the scaling functions, valid for any rank and κ. As an application, we analyze quantitatively the large 't Hooft coupling limit κ 1 where we identify all perturbative and non-perturbative contributions. The latter are associated with heavy electric BPS states and the precise correspondence with their mass spectrum is clarified. arXiv:2001.06645v2 [hep-th] 28 Jan 20201 The idea of a large charge/weak coupling compensation is closely related to the solvability of the BMN limit in AdS/CFT [4,5] and, more generally, to the coherent-state effective theory description of "semiclassical" string states [6,7] and its role in capturing the strong coupling regime [8].2 An equivalent statement is that an exact saddle point analysis is possible in the double scaling limit.

Section: Large R-charge Observablesmentioning

confidence: 99%

“…Take the interacting action S int (a), cf. (2.3), and convert tr R (•) into traces in the fundamental representation using the general relations derived in [34]. This allows to write…”

Section: Application To the Five N = 2 Superconformal Su (N ) Gauge Tmentioning

confidence: 99%

Section: Three Loop Diagram Analysis In N = 1 Superspacementioning

confidence: 99%

“…The next orders will be more and more involved. Diagrams built from C (4) , C (5) , C (6) will appear at g 6 order (see [34] for a g 6 analysis).…”

Section: A Field Theory Action and Feynman Rulesmentioning

confidence: 99%

Section: A1 Evaluation Of the Color Factorsmentioning

confidence: 99%

See 3 more Smart Citations

$$ \mathcal{N} $$ = 2 conformal gauge theories at large R-charge: the SU(N) case

Beccaria

Galvagno

Hasan

2020

Emitted radiation and geometry

Bianchi

Billó

Galvagno

et al. 2020

Self Cite

In conformal N = 2 Super Yang-Mills theory, the energy emitted by an accelerated heavy particle is computed by the one-point function of the stress tensor operator in the presence of a Wilson line. In this paper, we consider the theory on the ellipsoid and we prove a conjectured relation between the stress tensor one-point function and the first order expansion of the Wilson loop expectation value in the squashing parameter. To do this, we analyze the behavior of the Wilson loop for a small deformation of the background geometry and, at first order in the deformation, we fix the kinematics using defect CFT constraints. In the final part of the paper, we analyze the consequences of our results for the weak coupling perturbative expansion. In particular, comparing the weakly coupled matrix model with the ordinary Feynman diagram expansion, we find a natural transcendentality driven organization for the latter. Keywords: N = 2 conformal SYM theories, Wilson loops, Brehmsstrahlung, rigid supersymmetry dimensions has no scale, thus the straight Wilson line can be treated as a conformal defect. The emitted radiation is computed by slightly deforming the shape of the defect.As usual, things get harder when one considers non-Abelian gauge theories, which are strongly coupled at low energies and where conformality is broken by quantum corrections. In light of this complexity, it is useful to restrict our attention to those examples of strongly interacting gauge theories which preserve conformality. These cases typically come with a larger symmetry group which includes supersymmetry, making them much more tractable. For the maximally supersymmetric theory in four dimensions, N = 4 Super Yang Mills (SYM) theory, the combination of defect techniques and supersymmetric localization led to the derivation of a beautiful formula for the Bremsstrahlung function associated with the Maldacena Wilson loop [1,2], preserving half of the supercharges. Shortly after, the same result was confirmed by an integrability computation [3,4], providing one of the few examples of a quantity that is accessible to both techniques 1 . The work of [1] heavily relied on the interpretation of the Wilson line as a superconformal defect. In particular, it was pointed out that the Bremsstrahlung function can be computed as the two-point function of an important defect operator, called the displacement operator. Furthermore, the same quantity can be related to the small angle limit of the cusp anomalous dimension, thus providing an interesting connection with massive scattering amplitudes.Similar developments allowed to find an exact expression for the Bremsstrahlung function in ABJM theory [9], a three-dimensional relative of N = 4 SYM. In that case, two superconformal Wilson lines are known (see [10] for a recent review). The immediate generalization of the Maldacena Wilson loop turns out to be 1 6 BPS [11-13] and its Bremsstrahlung function was already proposed in [14]. The maximally supersymmetric case [15], instead, involves also fermionic couplings ...

Strong coupling expansions in $$ \mathcal{N} $$ = 2 quiver gauge theories

Billó

Frau

Lerda

et al. 2023

Self Cite

We study the 3-point functions of gauge-invariant scalar operators in four dimensional $$ \mathcal{N} $$ N = 2 superconformal quiver theories using supersymmetric localization in the planar limit of a large number of colors. By exploiting a web of nontrivial relations, we show that the 3-point functions can be expressed in terms of the 2-point functions through exact Ward-like identities that are valid for all values of the coupling constant. In this way, using recent results about the 2-point functions, we are able to obtain the asymptotic strong-coupling expansion of the 3-point functions and of the corresponding structure constants in the planar limit. Our results extend to sub-leading orders what has been recently found at leading order, where a precise match with calculations within the AdS/CFT correspondence at the supergravity level is possible. Therefore, our findings can be interpreted also as a prediction for the sub-leading string corrections to these holographic calculations.