Scalar QED in AdS

Abstract

We consider scalar QED with Nf flavors in AdSD. For D < 4 the theory is strongly-coupled in the IR. We use the spin 1 spectral representation to compute and efficiently resum the bubble diagram in AdS, in order to obtain the exact propagator of the photon at large Nf. We then apply this result to compute the boundary four-point function of the charged operators at leading order in 1/Nf and exactly in the coupling, both in the Coulomb and in the Higgs phase. In the first case a conserved current is exchanged in the four-point function, while in the second case the current is absent and there is a pattern of double-trace scaling dimension analogous to a resonance in flat space. We also consider the BCFT data associated to the critical point with bulk conformal symmetry separating the two phases. Both in ordinary perturbation theory and at large Nf, in integer dimension D = 3 an IR divergence breaks the conformal symmetry on the boundary by inducing a boundary RG flow in a current-current operator.

Analytic and numerical bootstrap for the long-range Ising model

“…An alternative justification for the ansatz (2.8) uses the recent theorem of [29] as follows. 5 As stated above, the trivial defect two-point function contains only '+' modes but the converse is true as well. Indeed, if we allow for '+' modes only, the resulting (connected) bulk two-point function of Φ is simply the unique Klein-Gordon propagator with regular boundary conditions on the defect dictated by the bulk-defect OPE, where the b Φ,+ s are fixed to reproduce the contact term in the bulk.…”

“…(2.11) 4 See appendix B for an explicit leading-order check of this fact. 5 We are grateful to Balt van Rees for discussions on this point. If (b Φ,± 0 ) 2 ≥ 0, which holds in unitary theories, a Φ 2 can be further constrained.…”

“…The importance of studying Conformal Field Theories (CFTs) without a stress tensor can be motivated from various angles. The past decade has seen a surge of interest in Quantum Field Theories (QFTs) that live on a fixed Anti-de Sitter (AdS) background [1][2][3][4][5][6][7][8]. Due to the lack of dynamical gravity, the CFT which encodes boundary correlation functions has…”

On partition functions and phases of scalars in AdS

“…While our works involved computation of two point functions at coincident AdS spatial points, two and higher point functions can be computed in general. These have been computed on Euclidean AdS for various theories in [15]- [16] and [40], [41]. For AdS with flat boundary, thermal correlators were studied in [42].…”

“…There have been recent works focusing on critical points of field theories in AdS which shed light on conformal field theories in flat space with boundaries [15]- [18]. Field theories with large number of flavors have been studied in [15] [16] [19] [20]. [21] and [22] explored RG flows in AdS.…”