Edward Witten generalizes some concepts of the Langlands program. In the simplest version of the program, one deals with flat connections on a Riemann surface. Adding simple poles in the connection is called "tame ramification" while adding stronger singularities is referred to as "wild ramification" which is the subject of Witten's paper. Stokes' phenomenon and isomonodromic deformation play a role in these new, largely heavily mathematical results.

Jafferis and Saulina compute BPS indices on Calabi-Yau manifolds equipped with two intersecting families of D4-branes. The intersection is a compact Riemann surface. They argue that their index, computed from a

*q*-deformed U(M) x U(N) gauge theory, computes a jump of an index involving one D4-brane that can just split into two on a wall of marginal stability.

Silva and Landim looked at a two-form in a curved spacetime. By Hodge duality, the theory is argued to be equivalent to a scalar and this fact holds even if interactions are taken into account. The stress-energy tensor is calculated.

Sasakura verifies a relationship between (primarily) two-dimensional tori obtained as solutions of general relativity and fuzzy tori. For this two-dimensional theory, he verifies that the "R" term doesn't contribute to the momentum-dependence of the fluctuations because it is topological which is why "R squared" gives the leading nonzero dependence.

Splittorff and Verbaarschot falsify the Banks-Casher formula for theories with the sign problem and work out the arguably correct replacement in the special case of one-dimensional QCD with a chemical potential. The sign problem is a situation when Monte-Carlo evaluation breaks down because the average phase factor (in a one-loop determinant etc.) vanishes in the thermodynamic limit.

Kinoshita constructs a warped dS4 x S4 compactification where the sphere is deformed and connects this new branch of solutions to the conventional unwarped branch with ordinary spheres.

Kitazawa and Nagaoka study the IKKT model in the way that I always considered correct. The IKKT model comes from type IIB D-instantons and has no time coordinate. So you shouldn't be looking for a Hamiltonian. Instead, you should view it as a tool to generate the S-matrix amplitudes beyond the perturbative expansion. To do so, you need vertex operators. At generic couplings, only the supergravity multiplet forms stable asymptotic states. They construct the vertex operators for these graviton states and connect them with the perturbative superstring graviton vertex operators. The matrix vertex operators have exactly the same form I have believed to be correct, namely the supertrace of an exponential of the matrix (k.X): recall that X is a matrix in the model. The exponential is multiplied by polynomials in the fundamental matrix fields before the supertrace is evaluated.

**Your humble correspondent thinks that this is today's most interesting paper.**

Maziashvili offers an entertaining interpretation of the gravitational loop corrections to the running gauge couplings: the naturally defined "spacetime dimension" slightly drops below four as you approach the Planck scale.

Schweigert and Tsouchnika classify equivalences between Wess-Zumino-Witten models and minimal models - the Krammers-Wannier dualities - and show that they only exist for small levels which is what you expected (or knew) anyway.

Castro, De Castro, Hott look at Dirac fermions in two dimensions coupled to scalars and pseudoscalars with (solvable) Pöschl-Teller-like potentials (tanh of a scalar etc.), with a special focus on how the dynamics depends on various signs in the potentials.

Morris shows that the essence of a recent geometrical idea due to Hitchin et al. has already been found by Warren Siegel in the 1990s. Recall that Hitchin et al. want to generalize geometry to make stringy T-duality O(d,d,Z) manifest by adding the "dual" (cotangent) dimension together with the "normal" (tangent) dimensions. They show that Siegel, in fact, went well beyond some geometric concepts when he studied an actual Lagrangian with these doubled degrees of freedom. Ten years ago, I was very attracted to these pictures where you add both "X" and "X-dual" at the same moment but I no longer think that these highly redundant descriptions are necessarily wise because one needs to impose a lot of constraints acting on the "extended space" that look unnatural (they're highly non-local, for example).

Fosco and Moreno look at three-dimensional noncommutative field theory with a scalar field and a certain interaction. The one-loop cosmological constant is expressed in terms of the coupling constant and a tree-level scattering amplitude. That's what usually happens for (n+1)-loop vacuum energy graphs... The rest of the one-loop effective action is derived, too.

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