TY - JOUR

T1 - The M-theory archipelago

AU - Agmon, Nathan B.

AU - Chester, Shai M.

AU - Pufu, Silviu S.

N1 - Funding Information:
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited
Publisher Copyright:
© 2020, The Author(s).

PY - 2020/2/1

Y1 - 2020/2/1

N2 - We combine supersymmetric localization results and the numerical conformal bootstrap technique to study the 3d maximally supersymmetric (N = 8) CFT on N coincident M2-branes (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.

AB - We combine supersymmetric localization results and the numerical conformal bootstrap technique to study the 3d maximally supersymmetric (N = 8) CFT on N coincident M2-branes (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.

KW - AdS-CFT Correspondence

KW - Conformal and W Symmetry

KW - Extended Supersymmetry

KW - M-Theory

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U2 - 10.1007/JHEP02(2020)010

DO - 10.1007/JHEP02(2020)010

M3 - Article

AN - SCOPUS:85079130632

SN - 1126-6708

VL - 2020

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 2

M1 - 10

ER -