Carving Out the End of the World or (Superconformal Bootstrap in Six Dimensions)

We bootstrap ${\cal N}=(1,0)$ superconformal field theories in six dimensions, by analyzing the four-point function of flavor current multiplets. Assuming $E_8$ flavor group, we present universal bounds on the central charge $C_T$ and the flavor central charge $C_J$. Based on the numerical data, we conjecture that the rank-one E-string theory saturates the universal lower bound on $C_J$, and numerically determine the spectrum of long multiplets in the rank-one E-string theory. We comment on the possibility of solving the higher-rank E-string theories by bootstrap and thereby probing M-theory on AdS${}_7\times{\rm S}^4$/$\mathbb{Z}_2$.Comment: 59 pages, 10 figures, 4 tables; v2-v5: typos corrected, references adde

Bootstrapping 2D CFTs in the Semiclassical Limit

We study two dimensional conformal field theories in the semiclassical limit. In this limit, the four-point function is dominated by intermediate primaries of particular weights along with their descendants, and the crossing equations simplify drastically. For a four-point function receiving sufficiently small contributions from the light primaries, the structure constants involving heavy primaries follow a universal formula. Applying our results to the four-point function of the $\mathbb Z_2$ twist field in the symmetric product orbifold, we produce the Hellerman bound and the logarithmically corrected Cardy formula that is valid for $h \geq c/12$.Comment: 32 pages, 7 figures. v2, v3: references added, minor clarification

Romans Supergravity from Five-Dimensional Holograms

We study five-dimensional superconformal field theories and their holographic dual, matter-coupled Romans supergravity. On the one hand, some recently derived formulae allow us to extract the central charges from deformations of the supersymmetric five-sphere partition function, whose large N expansion can be computed using matrix model techniques. On the other hand, the conformal and flavor central charges can be extracted from the six-dimensional supergravity action, by carefully analyzing its embedding into type I' string theory. The results match on the two sides of the holographic duality. Our results also provide analytic evidence for the symmetry enhancement in five-dimensional superconformal field theories.Comment: 57 pages, 4 figures, 6 tables; v2: references adde

Words to describe a black hole

We revamp the constructive enumeration of 1/16-BPS states in the maximally supersymmetric Yang-Mills in four dimensions, and search for ones that are not of multi-graviton form. A handful of such states are found for gauge group SU(2) at relatively high energies, resolving a decade-old enigma. Along the way, we clarify various subtleties in the literature, and prove a non-renormalization theorem about the exactness of the cohomological enumeration in perturbation theory. We point out a giant-graviton-like feature in our results, and envision that a deep analysis of our data will elucidate the fundamental properties of black hole microstates.Comment: 13 pages, 2 figures, 5 tables; v2, v3: minor revisions, references adde

Lorentzian Dynamics and Factorization Beyond Rationality

We investigate the emergence of topological defect lines in the conformal Regge limit of two-dimensional conformal field theory. We explain how a local operator can be factorized into a holomorphic and an anti-holomorphic defect operator connected through a topological defect line, and discuss implications on Lorentzian dynamics including aspects of chaos. We derive a formula relating the infinite boost limit, which holographically encodes the "opacity" of bulk scattering, to the action of topological defect lines on local operators. Leveraging the unitary bound on the opacity and the positivity of fusion coefficients, we show that the spectral radii of a large class of topological defect lines are given by their loop expectation values. Factorization also gives a formula relating the local and defect operator algebras, and fusion categorical data. We then review factorization in rational conformal field theory from a defect perspective, and examine irrational theories. On the orbifold branch of the $c = 1$ free boson theory, we find a unified description for the topological defect lines through which the twist fields are factorized; at irrational points, the twist fields factorize through "non-compact" topological defect lines which exhibit continuous defect operator spectra. Along the way, we initiate the development of a formalism to characterize non-compact topological defect lines.Comment: 41+30 pages, 2 figures, 2 tables; v2: significant updates, enriched discussion on non-compact TDLs, extended scope of opacity bound, added TDL fusion rule in orbifold theory; v3: minor revision; v4: added Proposition

Lorentzian Dynamics and Factorization Beyond Rationality

We investigate the emergence of topological defect lines in the conformal Regge limit of two-dimensional conformal field theory. We explain how a local operator can be factorized into a holomorphic and an anti-holomorphic defect operator connected through a topological defect line, and discuss implications on Lorentzian dynamics including aspects of chaos. We derive a formula for the infinite boost limit, which holographically encodes the transparency/opacity of bulk scattering, in terms of the action of topological defect lines on local operators, and argue for a unitarity bound. Factorization also gives a formula relating the local and defect operator algebras and fusion categorical data. We review factorization in rational conformal field theory from a defect perspective, and examine irrational theories. On the orbifold branch of the $c = 1$ free boson theory, a dichotomy between rationality and irrationality is found regarding the factorization of the twist field