$$ \mathcal{N} $$ = 2 conformal gauge theories at large R-charge: the SU(N) case
Matteo Beccaria, Francesco Galvagno, Azeem Hasan
Abstract
A bstract 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 $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 2 SU( N ) gauge theories with conformal matter content at large R-charge Q R → ∞ with fixed ’t Hooft-like coupling $$ \kappa ={Q}_{\mathrm{R}}{g}_{\mathrm{YM}}^2. $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>κ</mml:mi> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>Q</mml:mi> <mml:mi>R</mml:mi> </mml:msub> <mml:msubsup> <mml:mi>g</mml:mi> <mml:mi>YM</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mo>.</mml:mo> </mml:math> 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 $$ \frac{1}{2} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> </mml:math> -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 $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 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.