AdS Field Theory from Conformal Field Theory (original) (raw)

Effective conformal theory and the flat-space limit of AdS

Journal of High Energy Physics, 2011

We develop the idea of an effective conformal theory describing the low-lying spectrum of the dilatation operator in a CFT. Such an effective theory is useful when the spectrum contains a hierarchy in the dimension of operators, and a small parameter whose role is similar to that of 1/N in a large N gauge theory. These criteria insure that there is a regime where the dilatation operator is modified perturbatively. Global AdS is the natural framework for perturbations of the dilatation operator respecting conformal invariance, much as Minkowski space naturally describes Lorentz invariant perturbations of the Hamiltonian. Assuming that the lowest-dimension single-trace operator is a scalar, O, we consider the anomalous dimensions, γ(n, l), of the double-trace operators of the form O(∂ 2) n (∂) l O. Purely from the CFT we find that perturbative unitarity places a bound on these dimensions of |γ(n, l)| < 4. Non-renormalizable AdS interactions lead to violations of the bound at large values of n. We also consider the case that these interactions are generated by integrating out a heavy scalar field in AdS. We show that the presence of the heavy field "unitarizes" the growth in the anomalous dimensions, and leads to a resonancelike behavior in γ(n, l) when n is close to the dimension of the CFT operator dual to the heavy field. Finally, we demonstrate that bulk flat-space S-matrix elements can be extracted from the large n behavior of the anomalous dimensions. This leads to a direct connection between the spectrum of anomalous dimensions in d-dimensional CFTs and flatspace S-matrix elements in d + 1 dimensions. We comment on the emergence of flat-space locality from the CFT perspective.

The Goldstone equivalence theorem and AdS/CFT

Journal of High Energy Physics, 2015

The Goldstone equivalence theorem allows one to relate scattering amplitudes of massive gauge fields to those of scalar fields in the limit of large scattering energies. We generalize this theorem under the framework of the AdS/CFT correspondence. First, we obtain an expression of the equivalence theorem in terms of correlation functions of creation and annihilation operators by using an AdS wave function approach to the AdS/CFT dictionary. It is shown that the divergence of the nonconserved conformal current dual to the bulk gauge field is approximately primary when computing correlators for theories in which the masses of all the exchanged particles are sufficiently large. The results are then generalized to higher spin fields. We then go on to generalize the theorem using conformal blocks in two and four-dimensional CFTs. We show that when the scaling dimensions of the exchanged operators are large compared to both their spins and the dimension of the current, the conformal blocks satisfy an equivalence theorem.

On AdS/CFT correspondence beyond SUGRA

2007

This thesis deals with three corners of the AdS/CFT Correspondence that lie one step beyond the classical supergravity (SUGRA) approximation. We first explore the BMN limit of the duality and study, in particular, the behavior of field theoretic propagators in the corresponding Penrose limit. We unravel the semiclassical (WKB-) exactness of the propagators in the resulting plane wave background metric. Then, we address the limit of vanishing coupling of the conformal field theory (CFT) at large N. In the simplified scenario of Higher Spin/O(N) Vector Model duality, the conformal partial wave (CPW) expansion of scalar four-point functions are reorganized to make them suggestive of a bulk interpretation in term of a consistent truncated massless higher spin theory and their corresponding exchange Witten graphs. We also explore the connection to the interacting O(N) Vector Model at its infra-red fixed point, at leading large N. Finally, coming back to the gauge theory, we study the effect of a relevant double-trace deformations of the boundary CFT on the partition function and its dual bulk interpretation. We show how the one-loop computation in the Anti-de Sitter (AdS) space correctly reproduces the partition function and conformal anomaly of the boundary theory. In all, we get a clean test of the duality beyond the classical SUGRA approximation in the AdS bulk and at the corresponding next-to-leading 1/N order of the CFT at the conformal boundary.

Conformal quantum mechanics as the CFT1 dual to AdS2

Physics Letters B, 2011

A 0 + 1-dimensional candidate theory for the CFT1 dual to AdS2 is discussed. The quantum mechanical system does not have a ground state that is invariant under the three generators of the conformal group. Nevertheless, we show that there are operators in the theory that are not primary, but whose "non-primary character" conspires with the "non-invariance of the vacuum" to give precisely the correlation functions in a conformally invariant theory. I.

Nearly Conformal QCD and Ads/CFT

2006

The AdS/CFT correspondence is a powerful tool to study the properties of conformal QCD at strong coupling in terms of a higher dimensional dual gravity theory. The power-law falloff of scattering amplitudes in the non-perturbative regime and calculable hadron spectra follow from holographic models dual to QCD with conformal behavior at short distances and confinement at large distances. String modes and fluctuations about the AdS background are identified with QCD degrees of freedom and orbital excitations at the AdS boundary limit. A description of form factors in space and time-like regions and the behavior of light-front wave functions can also be understood in terms of a dual gravity description in the interior of AdS.

Lectures on Conformal Field Theory

2016

These lectures notes are based on courses given at National Taiwan University, National Chiao-Tung University, and National Tsing Hua University in the spring term of 2015. Although the course was offered primarily for graduate students, these lecture notes have been prepared for a more general audience. They are intended as an introduction to conformal field theories in various dimensions, with applications related to topics of particular interest: topics include the conformal bootstrap program, boundary conformal field theory, and applications related to the AdS/CFT correspondence. We assume the reader to be familiar with quantum mechanics at the graduate level and to have some basic knowledge of quantum field theory. Familiarity with string theory is not a prerequisite for this lectures, although it can only help.

AdS Dynamics from Conformal Field Theory

1998

We explore the extent to which a local string theory dynamics in anti-de Sitter space can be determined from its proposed Conformal Field Theory (CFT) description. Free fields in the bulk are constructed from the CFT operators, but difficulties are encountered when one attempts to incorporate interactions. We also discuss general features of black hole dynamics as seen from the CFT perspective. In particular, we argue that the singularity of AdS_3 black holes is resolved in the CFT description.

Aspects of the conformal operator product expansion in AdS/CFT correspondence

2000

We present a detailed analysis of a scalar conformal four-point function obtained from AdS/CFT correspondence. We study the scalar exchange graphs in AdS and discuss their analytic properties. Using methods of conformal partial wave analysis, we present a general procedure to study conformal four-point functions in terms of exchanges of scalar and tensor fields. The logarithmic terms in the four-point functions are connected to the anomalous dimensions of the exchanged fields. Comparison of the results from AdS graphs with the conformal partial wave analysis, suggests a possible general form for the operator product expansion of scalar fields in the boundary CFT.

One-loop conformal anomalies from AdS/CFT in the Schrödinger representation

Journal of High Energy Physics, 1999

We compute the conformal anomalies of boundary CFTs for scalar and fermionic fields propagating in AdS spacetime at one-loop. The coefficients are quantized, with values related to the mass-spectra for Kaluza-Klein compactifications of Supergravity on AdS 5 × S 5 and AdS 7 × S 4. Our approach interprets the partition function of fields on AdS spacetime in terms of wave-functionals that satisfy the functional Schrödinger equation.