Field Theory In AdS Research Articles

AdS bulk locality from sharp CFT bounds

It is a long-standing conjecture that any CFT with a large central charge and a large gap ∆gap in the spectrum of higher-spin single-trace operators must be dual to a local effective field theory in AdS. We prove a sharp form of this conjecture by deriving numerical bounds on bulk Wilson coefficients in terms of ∆gap using the conformal bootstrap. Our bounds exhibit the scaling in ∆gap expected from dimensional analysis in the bulk. Our main tools are dispersive sum rules that provide a dictionary between CFT dispersion relations and S-matrix dispersion relations in appropriate limits. This dictionary allows us to apply recently-developed flat-space methods to construct positive CFT functionals. We show how AdS4 naturally resolves the infrared divergences present in 4D flat-space bounds. Our results imply the validity of twice-subtracted dispersion relations for any S-matrix arising from the flat-space limit of AdS/CFT.

Effective field theory in AdS: Continuum regime, soft bombs, and IR emergence

We consider a scalar field in a slice of Lorentzian five-dimensional AdS at arbitrary energies. We show that the presence of bulk interactions separates the behavior of the theory into two different regimes: Kaluza-Klein and continuum. We determine the transition scale between these regimes and show that UV-brane correlation functions are independent of IR-brane-localized operators for four-momenta beyond this transition scale. The same bulk interactions that induce the transition also give rise to cascade decays. We study these cascade decays for the case of a cubic self-interaction in the continuum regime. We find that the cascade decay progresses slowly towards the IR region and gives rise to soft spherical final states, in accordance with former results from both gravity and CFT. We identify a recursion relation between integrated squared amplitudes of different leg numbers and thus evaluate the total rate. We find that cascade decays in the continuum regime are exponentially suppressed. This feature completes the picture of the IR brane as an emergent sector as seen from the UV brane. We briefly discuss consistency with the holographic dual description of glueballs and some implications for dark sector models.

Are tiny gauge couplings out of the Swampland?

There is significant evidence suggesting that continuous global symmetries are always gauged in quantum gravity. However, very weakly gauged symmetries seem global to an effective field theory expansion in powers of Newton’s constant. We show that, at least for Einsteinian quantum gravity on AdS, such extremely weak gaugings are indeed in the Swampland: consistency with AdS black hole thermodynamics requires the bulk gauge coupling g2 not to vanish faster than ∼ exp(−ℓd−1/G), where ℓ is the AdSd+1 radius and G is Newton’s constant as we take the G → 0 limit. This translates to a constraint in the dual large N CFT, namely, that the two-point function coefficient of the current CJ cannot grow faster than exp(N2) in the large N limit. We also recover a previously known logarithmic relationship between the cutoff of the effective field theory in AdS, Planck’s mass, and the AdS radius.

AdS field theory from conformal field theory

Abstract We provide necessary and sufficient conditions for a Conformal Field Theory to have a description in terms of a perturbative Effective Field Theory in AdS. The first two conditions are well-known: the existence of a perturbative ‘1/N ’ expansion and an approximate Fock space of states generated by a finite number of low-dimension operators. We add a third condition, that the Mellin amplitudes of the CFT correlators must be well- approximated by functions that are bounded by a polynomial at infinity in Mellin space, or in other words, that the Mellin amplitudes have an effective theory-type expansion. We explain the relationship between our conditions and unitarity, and provide an analogy with scattering amplitudes that becomes exact in the flat space limit of AdS. The analysis also yields a simple connection between conformal blocks and AdS diagrams, providing a new calculational tool very much in the spirit of the S-Matrix program. We also begin to explore the potential pathologies associated with higher spin fields in AdS by generalizing Weinberg’s soft theorems to AdS/CFT. The AdS analog of Weinberg’s argument constrains the interactions of conserved currents in CFTs, but there are potential loopholes that are unavailable to theories of massless higher spin particles in flat spacetime.

A NOTE ON SCALAR FIELD THEORY IN AdS3/CFT2

We consider a scalar field theory in AdS d+1, and introduce a formalism on surfaces at equal values of the radial coordinate. In particular, we define the corresponding conjugate momentum. We compute the Noether currents for isometries in the bulk, and perform the asymptotic limit on the corresponding charges. We then introduce Poisson brackets at the border, and show that the asymptotic values of the bulk scalar field and the conjugate momentum transform as conformal fields of scaling dimensions Δ- and Δ+, respectively, where Δ± are the standard parameters giving the asymptotic behavior of the scalar field in AdS. Then we consider the case d = 2, where we obtain two copies of the Virasoro algebra, with vanishing central charge at the classical level. An AdS3/CFT2 prescription, giving the commutators of the boundary CFT in terms of the Poisson brackets at the border, arises in a natural way. We find that the boundary CFT is similar to a generalized ghost system. We introduce two different ground states, and then compute the normal ordering constants and quantum central charges, which depend on the mass of the scalar field and the AdS radius. We discuss certain implications of the results.

The goldstone fields of interacting higher spin field theory in AdS(4)

A higher spin field theory on AdS(4) possesses a conformal theory on the boundary R(3) which can be identified with the critical O(N) sigma model of O(N) invariant fields only. The notions of quasiprimary and secondary fields can be carried over to the AdS theory. If de Donder’s gauge is applied, the traceless part of the higher spin field on AdS(4) is quasiprimary and the Goldstone fields are quasiprimary fields to leading order too. Those fields corresponding to the Goldstone fields in the critical O(N) sigma model are odd-rank symmetric tensor currents which vanish in the free-field limit.

Flavor quarks inAdS4and gauge/gravity correspondence

The nonperturbative properties of gauge theories in AdS{sub 4} are studied in dual supergravity by including light flavor quarks, which are introduced by a D7-brane embedding. Contrary to the Minkowski and dS{sub 4}, the dilaton does not play any important dynamical role in the AdS{sub 4} case, and the characteristic properties like quark confinement and chiral symmetry breaking are realized mainly due to the geometry AdS{sub 4}. The possible hadron spectra are also examined, and we find that the meson spectra are well described by the formula given by the field theory in AdS{sub 4}, but the characteristic mass scale is modified by the gauge interactions for excited states.