Built on

W. Boucher, D. Friedan, and A. Kent, Determinant Formulae and Unitarity for the N=2 Superconformal Algebras in Two-Dimensions or Exact Results on String Compactification
1986
Earlier work this paper cites.
J. D. Brown and M. Henneaux, Central Charges in the Canonical Realization of Asymptotic Symmetries: An Example from Three-Dimensional Gravity
1986
Earlier work this paper cites.
I. Antoniadis, C. Bachas, C. Kounnas, and P. Windey, Supersymmetry Among Free Fermions and Superstrings
1986
Earlier work this paper cites.
P. Windey, Super Kac-moody Algebras and Supersymmetric Two-dimensional Free Fermions
1986
Earlier work this paper cites.
S. D. Mathur, S. Mukhi, and A. Sen, On the Classification of Rational Conformal Field Theories
1988
Earlier work this paper cites.
S. Odake, Character Formulas of an Extended Superconformal Algebra Relevant to String Compactification
1990
Earlier work this paper cites.
S. Odake, C = 3- d d Conformal Algebra With Extended Supersymmetry
1990
Earlier work this paper cites.
G. Hoehn, Selbstduale vertexoperatorsuperalgebren und das babymonster (self-dual vertex operator super algebras and the baby monster)
Original
1996
Earlier work this paper cites.
J. M. Maldacena, The Large N limit of superconformal field theories and supergravity
1998
Earlier work this paper cites.
S. S. Gubser, I. R. Klebanov, and A. M. Polyakov, Gauge theory correlators from noncritical string theory
1998
Earlier work this paper cites.
E. Witten, Anti-de Sitter space and holography
1998
Earlier work this paper cites.
N. Arkani-Hamed, L. Motl, A. Nicolis, and C. Vafa, The String landscape, black holes and gravity as the weakest force
2007
Earlier work this paper cites.
H. Ooguri and C. Vafa, On the Geometry of the String Landscape and the Swampland
2007
Earlier work this paper cites.

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2018

Modular Constraints on Superconformal Field Theories

Bae, Jin-Beom, Lee, Sungjay, Song, Jaewon

Understand

We constrain the spectrum of $\mathcal{N}=(1, 1)$ and $\mathcal{N}=(2, 2)$ superconformal field theories in two-dimensions by requiring the NS-NS sector partition function to be invariant under the $\Gamma_\theta$ congruence subgroup of the full modular group $SL(2, \mathbb{Z})$.

We employ semi-definite programming to find constraints on the allowed spectrum of operators with or without $U(1)$ charges.
Especially, the upper bounds on the twist gap for the non-current primaries exhibit interesting peaks, kinks, and plateau.
We identify a number of candidate rational (S)CFTs realized at the numerical boundaries and find that they are realized as the solutions to modular differential equations associated to $\Gamma_\theta$.

Built on

W. Boucher, D. Friedan, and A. Kent, Determinant Formulae and Unitarity for the N=2 Superconformal Algebras in Two-Dimensions or Exact Results on String Compactification
1986
Earlier work this paper cites.
J. D. Brown and M. Henneaux, Central Charges in the Canonical Realization of Asymptotic Symmetries: An Example from Three-Dimensional Gravity
1986
Earlier work this paper cites.
I. Antoniadis, C. Bachas, C. Kounnas, and P. Windey, Supersymmetry Among Free Fermions and Superstrings
1986
Earlier work this paper cites.
P. Windey, Super Kac-moody Algebras and Supersymmetric Two-dimensional Free Fermions
1986
Earlier work this paper cites.
S. D. Mathur, S. Mukhi, and A. Sen, On the Classification of Rational Conformal Field Theories
1988
Earlier work this paper cites.
S. Odake, Character Formulas of an Extended Superconformal Algebra Relevant to String Compactification
1990
Earlier work this paper cites.
S. Odake, C = 3- d d Conformal Algebra With Extended Supersymmetry
1990
Earlier work this paper cites.
G. Hoehn, Selbstduale vertexoperatorsuperalgebren und das babymonster (self-dual vertex operator super algebras and the baby monster)
Original
1996
Earlier work this paper cites.
J. M. Maldacena, The Large N limit of superconformal field theories and supergravity
1998
Earlier work this paper cites.
S. S. Gubser, I. R. Klebanov, and A. M. Polyakov, Gauge theory correlators from noncritical string theory
1998
Earlier work this paper cites.
E. Witten, Anti-de Sitter space and holography
1998
Earlier work this paper cites.
N. Arkani-Hamed, L. Motl, A. Nicolis, and C. Vafa, The String landscape, black holes and gravity as the weakest force
2007
Earlier work this paper cites.
H. Ooguri and C. Vafa, On the Geometry of the String Landscape and the Swampland
2007
Earlier work this paper cites.