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We study constraints coming from the modular invariance of the partition function of two-dimensional conformal field theories. We constrain the spectrum of CFTs in the presence of holomorphic and anti-holomorphic currents using the semi-definite programming. In particular, we find the bounds on the twist gap for the non-current primaries depend dramatically on the presence of holomorphic currents, showing numerous kinks and peaks. Various rational CFTs are realized at the numerical boundary of the twist gap, saturating the upper limits on the degeneracies. Such theories include Wess-Zumino-Witten models for the Delignes exceptional series, the Monster CFT and the Baby Monster CFT. We also study modular constraints imposed by $mathcal{W}$-algebras of various type and observe that the bounds on the gap depend on the choice of $mathcal{W}$-algebra in the small central charge region.
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
We derive constraints on three-point functions involving the stress tensor, $T$, and a conserved $U(1)$ current, $j$, in 2+1 dimensional conformal field theories that violate parity, using conformal collider bounds introduced by Hofman and Maldacena.
We define Modular Linear Differential Equations (MLDE) for the level-two congruence subgroups $Gamma_vartheta$, $Gamma^0(2)$ and $Gamma_0(2)$ of $text{SL}_2(mathbb Z)$. Each subgroup corresponds to one of the spin structures on the torus. The pole st
In this work we investigate the matrix elements of the energy-momentum tensor for massless on-shell states in four-dimensional unitary, local, and Poincare covariant quantum field theories. We demonstrate that these matrix elements can be parametrise
Supersymmetric theories with the same bosonic content but different fermions, aka emph{twins}, were thought to exist only for supergravity. Here we show that pairs of super conformal field theories, for example exotic $mathcal{N}=3$ and $mathcal{N}=1