Large-N correlation functions in N $$ \mathcal{N} $$ = 2 superconformal QCD

131

We consider the 1/2 BPS circular Wilson loop in a generic N = 2 SU(N ) SYM theory with conformal matter content. We study its vacuum expectation value, both at finite N and in the large-N limit, using the interacting matrix model provided by localization results. We single out some families of theories for which the Wilson loop vacuum expectation values approaches the N = 4 result in the large-N limit, in agreement with the fact that they possess a simple holographic dual. At finite N and in the generic case, we explicitly compare the matrix model result with the field-theory perturbative expansion up to order g 8 for the terms proportional to the Riemann value ζ(5), finding perfect agreement. Organizing the Feynman diagrams as suggested by the structure of the matrix model turns out to be very convenient for this computation.

Section: Introductionmentioning

confidence: 99%

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

Billó

Galvagno

Lerda

2019

131

“…1 The drawback is that finite N results may display a deceiving complexity for large R-charge. For a discussion of what simplifications occur in the mixing problem at large N see [20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Double scaling limit of $$ \mathcal{N} $$= 2 chiral correlators with Maldacena-Wilson loop

Beccaria

2019

We consider N = 2 conformal QCD in four dimensions and the one-point correlator of a class of chiral primaries with the circular 1 2 -BPS Maldacena-Wilson loop. We analyze a recently introduced double scaling limit where the gauge coupling is weak while the R-charge of the chiral primary Φ is large. In particular, we consider the case Φ = (Trϕ 2 ) n , where ϕ is the complex scalar in the vector multiplet. The correlator defines a non-trivial scaling function at fixed κ = n g 2 YM and large n that may be studied by localization. For any gauge group SU (N ) we provide the analytic expression of the first correction ∼ ζ(3) κ 2 and prove its universality. In the SU (2) and SU (3) theories we compute the scaling functions at order O(κ 6 ). Remarkably, in the SU (2) case the scaling function is equal to an analogous quantity describing the chiral 2-point functions ΦΦ in the same large Rcharge limit. We conjecture that this SU (2) scaling function is computed at all-orders by a N = 4 SYM expectation value of a matrix model object characterizing the one-loop contribution to the 4sphere partition function. The conjecture provides an explicit series expansion for the scaling function and is checked at order O(κ 10 ) by showing agreement with the available data in the sector of chiral 2-point functions.

“…The latter is in turn completely determined by the two-and three-point functions of chiral primary operators [8]. Thanks to recent developments, these correlation functions are now computable in several 4d N = 2 SCFTs [9,10,[24][25][26][27][28][29]. Therefore, these results can now be interpreted as an exact determination of the Berry curvature for the chiral primary states of these theories.…”

Section: Berry Phase In 4d N = 2 Scftsmentioning

confidence: 97%

Aspects of Berry phase in QFT

Baggio

Niarchos

Papadodimas

2017

Self Cite

When continuous parameters in a QFT are varied adiabatically, quantum states typically undergo mixing -a phenomenon characterized by the Berry phase. We initiate a systematic analysis of the Berry phase in QFT using standard quantum mechanics methods. We show that a non-trivial Berry phase appears in many familiar QFTs. We study a variety of examples including free electromagnetism with a theta angle, and certain supersymmetric QFTs in two and four spacetime dimensions. We also argue that a large class of QFTs with rich Berry properties is provided by CFTs with non-trivial conformal manifolds. Using the operator-state correspondence we demonstrate in this case that the Berry connection is equivalent to the connection on the conformal manifold derived previously in conformal perturbation theory. In the special case of chiral primary states in 2d N = (2, 2) and 4d N = 2 SCFTs the Berry phase is governed by the tt * equations. We present a technically useful rederivation of these equations using quantum mechanics methods.