Juan Maldacena

A bstract: We consider a quantum mechanical model involving interacting fermions without disorder that has the same low energy physics as the supersymmetric SYK model. The model is SU(2) invariant, and the supercharge involves the SU(2) 3j symbol. We analyze various solvable corners, conceptually explain why it has a melonic expansion, and perform an exact diagonalization for small values of N . Expanded around the states with maximal angular momentum, the model is approximated by a two dimensional CFT. The BPS states have a simple description in that regime.

The sphere partition function is one of the simplest Euclidean gravity computations. It is usually interpreted as count of states. However, the one loop gravity correction contains a dimension dependent phase factor, [Formula: see text], which seems confusing for such an interpretation. We show that, after including an observer, this phase cancels for the quantity that should correspond to a count of states.

A bstract: We compute the phase of the Euclidean gravity partition function on manifolds of the form S ^p × M _q . We find that the total phase is equal to the phase in pure gravity on S ^p times an extra phase that arises from negative mass squared fields that we obtain when we perform a Kaluza-Klein reduction to S ^p . The latter can be matched to the phase expected for physical negative modes seen by a static path observer in dS _p . In the case of S ^p × S ^q the answer can be interpreted in terms of a computation in the static patch of dS _p or dS _q . We also provide the phase when we have a product of many spheres. We clarify the procedure for determining the precise phase factor. We discuss some aspects of the interpretation of this phase.

We discuss a no-boundary proposal for a subregion of the universe. In the classical approximation, this density matrix involves finding a specific classical solution of the equations of motion with no boundary. Beyond the usual no boundary condition at early times, we also have another no boundary condition in the region we trace out. We can find the prescription by starting from the usual Hartle-Hawking proposal for the wavefunction on a full slice and tracing out the unobserved region in the classical approximation. We discuss some specific subregions and compute the corresponding solutions. These geometries lead to phenomenologically unacceptable probabilities, as expected. We also discuss how the usual Coleman de Luccia bubble solutions can be interpreted as a possible no boundary contribution to the density matrix of the universe. These geometries lead to local (but not global) maxima of the probability that are phenomenologically acceptable.

We show that the Banks-Fischler-Shenker-Susskind matrix model for M-theory obeys the leading and subleading soft theorems expected from eleven-dimensional supergravity. The subleading soft theorem implies the amplitude is Lorentz symmetric. This is argued for general four point amplitudes, but only for restricted kinematics for five and higher point amplitudes.

We compute the three graviton amplitude in the Banks-Fischler-Shenker-Susskind matrix model for M-theory. Even though the three point amplitude is determined by super Poincare invariance in eleven dimensional M-theory, it requires a non-trivial computation in the matrix model. We consider a configuration where all three gravitons carry non-zero longitudinal momentum. To simplify the problem, we compactify one additional dimension and relate the amplitude to a supersymmetric index computation. We find agreement with the expected answer even at finite values of N.

We study the gravity solution dual to the D0 brane quantum mechanics, or BFSS matrix model, in the ’t Hooft limit.The classical physics described by this gravity solution is invariant under a scaling transformation, which changes the action with a specific critical exponent, sometimes called the hyperscaling violating exponent. We present an argument for this critical exponent from the matrix model side, which leads to an explanation for the peculiar temperature dependence of the entropy in this theory, S ∝ T^9/5. We also present a similar argument for all other Dp-brane geometries.We then compute the black hole quasinormal modes. This involves perturbing the finite temperature geometry. These perturbations can be easily obtained by a mathematical trick where we view the solution as the dimensional reduction of an Ad_S2+9/5× S⁸ geometry.