AdS4/CFT3 for unprotected operators

131

155

We develop new techniques to compute five-point correlation functions from IIB supergravity on AdS 5 × S 5. Our methods rely entirely on symmetry and general consistency conditions, and eschew detailed knowledge of the supergravity effective action. We demonstrate our methods by computing the five-point function of the 20 operator, which is the superconformal primary of the stress tensor multiplet. We also develop systematic methods to compute the five-point conformal blocks in series expansions. Using the explicit expressions of the conformal blocks, we perform a Euclidean OPE analysis of the 20 five-point function. We find expected agreement with non-renormalized quantities and also extract new CFT data at strong coupling.

Section: Jhep10(2019)247mentioning

confidence: 52%

“…While the AdS 5 × S 5 background has attracted most attention, many interesting results have been obtained for other string theory/M-theory backgrounds as well. See [18][19][20][21][22][23][24][25][26][27][28][29] for some recent developments.…”

Section: Jhep10(2019)247mentioning

confidence: 99%

20′ five-point function from AdS5× S5 supergravity

Gonçalves¹,

Pereira²,

Zhou³

2019

131

155

“…For whichever of these theories saturates the bound in the infinite precision limit, all the CFT data in S 2 S 2 S 2 S 2 , both protected and unprotected, could then be numerically determined using the extremal functional method [59][60][61]. To leading order in 1/c T , where all ABJ(M) theories are indistinguishable, the bootstrap predictions were verified by supergravity calculations of lowest twist unprotected operators [62,63] and even more non-trivially subleading twist unprotected operators [63].…”

Section: Introductionmentioning

confidence: 94%

The M-theory archipelago

Agmon

Chester

Pufu

2020

Self Cite

105

We combine supersymmetric localization results and the numerical conformal bootstrap technique to study the 3d maximally supersymmetric (N = 8) CFT on N coincident M2branes (the U (N ) k × U (N ) −k ABJM theory at Chern-Simons level k = 1). In particular, we perform a mixed correlator bootstrap study of the superconformal primaries of the stress tensor multiplet and of the next possible lowest-dimension half-BPS multiplet that is allowed by 3d N = 8 superconformal symmetry. Of all known 3d N = 8 SCFTs, the k = 1 ABJM theory is the only one that contains both types of multiplets in its operator spectrum. By imposing the values of the short OPE coefficients that can be computed exactly using supersymmetric localization, we are able to derive precise islands in the space of semi-short OPE coefficients for an infinite number of such coefficients. We find that these islands decrease in size with increasing N . More generally, we also analyze 3d N = 8 SCFT that contain both aforementioned multiplets in their operator spectra without inputing any additional information that is specific to ABJM theory. For such theories, we compute upper and lower bounds on the semi-short OPE coefficients as well as upper bounds on the scaling dimension of the lowest unprotected scalar operator. These latter bounds are more constraining than the analogous bounds previously derived from a single correlator bootstrap of the stress tensor multiplet. This leads us to conjecture that the U (N ) 2 × U (N + 1) −2 ABJ theory, and not the k = 1 ABJM theory, saturates the single correlator bounds. July 2019correlator system that is the primary focus of this paper has three advantages:1. In principle, the free multiplet S 1 is allowed to appear in the mixed OPE S 2 × S 3 , so 3 Lower bounds can be computed for the OPE coefficients of the operators that have been assumed to be relevant, since there is now a gap between them and the continuum of irrelevant operators. Islands in the space of these OPE coefficients are reported in [14,17].4 Note that for 4d SCFTs with N ≥ 3, all the protected operators that appear in the four-point function of half-BPS operator are already fixed by the 2d chiral algebra [36], so the bootstrap studies [37-39] could not compute any upper bounds on OPE coefficients. 5 Percent error as computed, for instance, in (4.13). 6 Here, Λ is a parameter counting the number of derivatives in the functionals used for numerical bootstrap. See [41] for the precise definition. 9 Our blocks are normalized as G k12,k34 ∆, (r, η) ∼ r ∆ P (η) as r → 0, where P (η) is a Legendre polynomial.

“…into which we insert (the precise forms of) (11) and (13) to obtain sums of terms of the form k α (z)k β (1 −z) and k α (1 −z)k β (z). To extract a purely numerical recursion relation we then multiply the resulting equation by…”

Section: Recursionmentioning

confidence: 99%

“…A strategy for fixing the coefficients using a chiral algebra conjecture [10] was recently proposed in [11]. Moreover, the M-theory effective action can also be deduced from correlators of the ABJM theory [12], which is dual to M-theory in AdS 4 ×S 7 [13,14]. As a warm-up for our analysis in the (2, 0) theory, we first derive recursion relations for anomalous dimensions in an abstract non-supersymmetric 6d conformal field theory (CFT), which we match against the conformal block expansion of Witten diagrams for a massive scalar field in AdS 7 .…”

Section: Introductionmentioning

confidence: 99%

Recursion relations for anomalous dimensions in the 6d (2, 0) theory

Abl

Heslop

Lipstein

2019

We derive recursion relations for the anomalous dimensions of double-trace operators occurring in the conformal block expansion of four-point stress tensor correlators in the 6d (2, 0) theory, which encode higher-derivative corrections to supergravity in AdS 7 × S 4 arising from M-theory. As a warm-up, we derive analogous recursion relations for four-point functions of scalar operators in a toy non-supersymmetric 6d conformal field theory.