TY - JOUR
T1 - Exact correlators of BPS Operators from the 3d superconformal bootstrap
AU - Chester, Shai M.
AU - Lee, Jaehoon
AU - Pufu, Silviu S.
AU - Yacoby, Ran
N1 - Funding Information:
We thank Ofer Aharony, Victor Mikhaylov, and Leonardo Rastelli for useful discussions. The work of SMC, SSP, and RY was supported in part by the US NSF under Grant No. PHY-1418069. The work of JL was supported in part by the U.S. Department of Energy under cooperative research agreement Contract Number DE-SC00012567.
Publisher Copyright:
© 2015, The Author(s).
PY - 2015/3/1
Y1 - 2015/3/1
N2 - Abstract: We use the superconformal bootstrap to derive exact relations between OPE coefficients in three-dimensional superconformal field theories with (Formula presented.) supersymmetry. These relations follow from a consistent truncation of the crossing symmetry equations that is associated with the cohomology of a certain supercharge. In (Formula presented.) SCFTs, the non-trivial cohomology classes are in one-to-one correspondence with certain half-BPS operators, provided that these operators are restricted to lie on a line. The relations we find are powerful enough to allow us to determine an infinite number of OPE coefficients in the interacting SCFT (U(2)2× U(1)−2 ABJ theory) that constitutes the IR limit of O(3) (Formula presented.) super-Yang-Mills theory. More generally, in (Formula presented.) SCFTs with a unique stress tensor, we are led to conjecture that many superconformal multiplets allowed by group theory must actually be absent from the spectrum, and we test this conjecture in known (Formula presented.) SCFTs using the superconformal index. For generic (Formula presented.) SCFTs, we also improve on numerical bootstrap bounds on OPE coefficients of short and semi-short multiplets and discuss their relation to the exact relations between OPE coefficients we derived. In particular, we show that the kink previously observed in these bounds arises from the disappearance of a certain quarter-BPS multiplet, and that the location of the kink is likely tied to the existence of the U(2)2× U(1)−2 AJ theory, which can be argued to not possess this multiplet.
AB - Abstract: We use the superconformal bootstrap to derive exact relations between OPE coefficients in three-dimensional superconformal field theories with (Formula presented.) supersymmetry. These relations follow from a consistent truncation of the crossing symmetry equations that is associated with the cohomology of a certain supercharge. In (Formula presented.) SCFTs, the non-trivial cohomology classes are in one-to-one correspondence with certain half-BPS operators, provided that these operators are restricted to lie on a line. The relations we find are powerful enough to allow us to determine an infinite number of OPE coefficients in the interacting SCFT (U(2)2× U(1)−2 ABJ theory) that constitutes the IR limit of O(3) (Formula presented.) super-Yang-Mills theory. More generally, in (Formula presented.) SCFTs with a unique stress tensor, we are led to conjecture that many superconformal multiplets allowed by group theory must actually be absent from the spectrum, and we test this conjecture in known (Formula presented.) SCFTs using the superconformal index. For generic (Formula presented.) SCFTs, we also improve on numerical bootstrap bounds on OPE coefficients of short and semi-short multiplets and discuss their relation to the exact relations between OPE coefficients we derived. In particular, we show that the kink previously observed in these bounds arises from the disappearance of a certain quarter-BPS multiplet, and that the location of the kink is likely tied to the existence of the U(2)2× U(1)−2 AJ theory, which can be argued to not possess this multiplet.
KW - Conformal and W Symmetry
KW - Extended Supersymmetry
KW - Topological Field Theories
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U2 - 10.1007/JHEP03(2015)130
DO - 10.1007/JHEP03(2015)130
M3 - Article
AN - SCOPUS:84958243374
SN - 1126-6708
VL - 2015
SP - 1
EP - 55
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
IS - 3
M1 - 130
ER -