Universal bounds on charged states in 2d CFT and 3d gravity

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 Deligne's exceptional series, the Monster CFT and the Baby Monster CFT. We also study modular constraints imposed by W-algebras of various type and observe that the bounds on the gap depend on the choice of W-algebra in the small central charge region.

Section: Jhep12(2017)045supporting

confidence: 66%

Modular constraints on conformal field theories with currents

Bae

Lee

Song

2017

“…We regard this as a version of the WGC in three dimensions. The recent work [30] also uses modular invariance to place an upper bound on the conformal dimension of charged operators, in a more general setting than the one we consider (the results of [30] are also valid for a noncompact gauge group, whereas ours rely on compactness in an essential way).…”

Section: Jhep10(2016)159mentioning

confidence: 99%

“…This will allow us to define a black hole threshold (see e.g. [30]) for operators corresponding to charged BTZ black holes in subsection 4.2, which is the CFT version of an extremality bound.…”

Section: Jhep10(2016)159mentioning

confidence: 99%

The Weak Gravity Conjecture in three dimensions

Montero

Shiu

Soler

2016

169

194

We study weakly coupled U(1) theories in AdS 3 , their associated charged BTZ solutions, and their charged spectra. We find that modular invariance of the holographic dual two-dimensional CFT and compactness of the gauge group together imply the existence of charged operators with conformal dimension significantly below the black hole threshold. We regard this as a form of the Weak Gravity Conjecture (WGC) in three dimensions. We also explore the constraints posed by modular invariance on a particular discrete Z N symmetry which arises in our discussion. In this case, modular invariance does not guarantee the existence of light Z N -charged states. We also highlight the differences between our discussion and the usual heuristic arguments for the WGC based on black hole remnants.

“…The blocks are also the basic components of the conformal bootstrap program [16][17][18][19][20]. Knowing their explicit forms would greatly assist the study of 2d CFTs and 3d gravity using the bootstrap [5,[21][22][23][24][25][26].…”

Section: Jhep03(2017)167mentioning

confidence: 99%

Degenerate operators and the 1/c expansion: Lorentzian resummations, high order computations, and super-Virasoro blocks

Chen

Fitzpatrick

Kaplan

et al. 2017

Self Cite

Abstract:One can obtain exact information about Virasoro conformal blocks by analytically continuing the correlators of degenerate operators. We argued in recent work that this technique can be used to explicitly resolve information loss problems in AdS 3 /CFT 2 . In this paper we use the technique to perform calculations in the small 1/c ∝ G N expansion:(1) we prove the all-orders resummation of logarithmic factors ∝ 1 c log z in the Lorentzian regime, demonstrating that 1/c corrections directly shift Lyapunov exponents associated with chaos, as claimed in prior work, (2) we perform another all-orders resummation in the limit of large c with fixed cz, interpolating between the early onset of chaos and late time behavior, (3) we explicitly compute the Virasoro vacuum block to order 1/c 2 and 1/c 3 with external dimensions fixed, corresponding to 2 and 3 loop calculations in AdS 3 , and (4) we derive the heavy-light vacuum blocks in theories with N = 1, 2 superconformal symmetry.