Beyond a=ca=c: Gravitational Couplings to Matter and the Stress Tensor OPE

We derive constraints on the operator product expansion of two stress tensors in conformal field theories (CFTs), both generic and holographic. We point out that in large $N$ CFTs with a large gap to single-trace higher spin operators, the stress tensor sector is not only universal, but isolated: that is, $\langle TT{\cal O}\rangle=0$, where ${\cal O}\neq T$ is a single-trace primary. We show that this follows from a suppression of $\langle TT{\cal O}\rangle$ by powers of the higher spin gap, $\Delta_{\rm gap}$, dual to the bulk mass scale of higher spin particles, and explain why $\langle TT{\cal O}\rangle$ is a more sensitive probe of $\Delta_{\rm gap}$ than $a-c$ in 4d CFTs. This result implies that, on the level of cubic couplings, the existence of a consistent truncation to Einstein gravity is a direct consequence of the absence of higher spins. By proving similar behavior for other couplings $\langle T{\cal O}_1{\cal O}_2\rangle$ where ${\cal O}_i$ have spin $s_i\leq 2$, we are led to propose that $1/\Delta_{\rm gap}$ is the CFT "dual" of an AdS derivative in a classical action. These results are derived by imposing unitarity on mixed systems of spinning four-point functions in the Regge limit. Using the same method, but without imposing a large gap, we derive new inequalities on these three-point couplings that are valid in any CFT. These are generalizations of the Hofman-Maldacena conformal collider bounds. By combining the collider bound on $TT$ couplings to spin-2 operators with analyticity properties of CFT data, we argue that all three tensor structures of $\langle TTT\rangle$ in the free-field basis are nonzero in interacting CFTs.Comment: 42+25 pages. v2: added refs, minor change

A complex structure on the moduli space of rigged Riemann surfaces

The study of Riemann surfaces with parametrized boundary components was initiated in conformal field theory (CFT). Motivated by general principles from Teichmueller theory, and applications to the construction of CFT from vertex operator algebras, we generalize the parametrizations to quasisymmetric maps. For a precise mathematical definition of CFT (in the sense of G. Segal), it is necessary that the moduli space of these Riemann surfaces be a complex manifold, and the sewing operation be holomorphic. We report on the recent proofs of these results by the authors

Open spin chains for giant gravitons and relativity

We study open spin chains for strings stretched between giant graviton states in the N=4 SYM field theory in the collective coordinate approach. We study the boundary conditions and the effective Hamiltonian of the corresponding spin chain to two loop order. The ground states of the spin chain have energies that match the relativistic dispersion relation characteristic of massive W boson particles on the worldvolume of the giant graviton configurations, up to second order in the limit where the momentum is much larger than the mass. We find evidence for a non-renormalization theorem for the ground state wave function of this spin chain system. We also conjecture a generalization of this result to all loop orders which makes it compatible with a fully relativistic dispersion relation. We show that the conjecture follows if one assumes that the spin chain admits a central charge extension that is sourced by the giant gravitons, generalizing the giant magnon dispersion relation for closed string excitations. This provides evidence for ten dimensional local physics mixing AdS directions and the five-sphere emerging from an N=4 SYM computation in the presence of a non-trivial background (made of D-branes) that break the conformal field theory of the system.Comment: 48 pages, 3 figures. v2: typos fixe

A simple mechanism for higher-order correlations in integrate-and-fire neurons

The collective dynamics of neural populations are often characterized in terms of correlations in the spike activity of different neurons. Open questions surround the basic nature of these correlations. In particular, what leads to higher-order correlations -- correlations in the population activity that extend beyond those expected from cell pairs? Here, we examine this question for a simple, but ubiquitous, circuit feature: common fluctuating input arriving to spiking neurons of integrate-and-fire type. We show that leads to strong higher-order correlations, as for earlier work with discrete threshold crossing models. Moreover, we find that the same is true for another widely used, doubly-stochastic model of neural spiking, the linear-nonlinear cascade. We explain the surprisingly strong connection between the collective dynamics produced by these models, and conclude that higher-order correlations are both broadly expected and possible to capture with surprising accuracy by simplified (and tractable) descriptions of neural spiking