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We present a quantum field theoretic description on the t−J model on a square lattice with dilute holes (i.e. near half-filling), based on the compact mutual Chern-Simons gauge theory. We show that, due to the presence of non-perturbative monopole plasma configuration from the antiferromagnetic background, holons (carrying electric charge) are linearly confined and strongly localized even without extrinsic disorder taken into account. Accordingly, the translation symmetry is spontaneously broken at ground state. Such an exotic localization is distinct from Anderson localization and essentially rooted in intrinsic Mott physics of the t−J model. Finally, a finite-temperature phase diagram is proposed. The metal-insulator transition observed in in-plane resistivity measurement is identified to a confinement-deconfinement transition from the perspective of gauge theory. The transition is characterized by the order parameter "Polyakov-line".

We construct the boundary phase space in D-dimensional Einstein gravity with a generic given co-dimension one null surface N as the boundary. The associated boundary symmetry algebra is a semi-direct sum of diffeomorphisms of \mathcal{N} and Weyl rescalings. It is generated by D towers of surface charges that are generic functions over \mathcal{N}. These surface charges can be rendered integrable for appropriate slicings of the phase space, provided there is no graviton flux through \mathcal{N}. In one particular slicing of this type, the charge algebra is the direct sum of the Heisenberg algebra and diffeomorphisms of the transverse space, \mathcal{N}_v for any fixed value of the advanced time v. Finally, we introduce null surface expansion- and spin-memories, and discuss associated memory effects that encode the passage of gravitational waves through \mathcal{N}, imprinted in a change of the surface charges.

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 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 ≥ c/12.

We construct an index for BPS operators supported on a ray in five dimensional superconformal field theories with exceptional global symmetries. We compute the E_n representations (for n = 2, . . . , 7) of operators of low spin, thus verifying that while the expression for the index is only SO(2n − 2) × U(1) invariant, the index itself exhibits the full E_n symmetry (at least up to the order we expanded). The ray operators we studied in 5d can be viewed as generalizations of operators constructed in a Yang-Mills theory with fundamental matter by attaching an open Wilson line to a quark. For n ≤ 7, in contrast to local operators, they carry nontrivial charge under the ℤ_{9 − n}  ⊂ E_n center of the global symmetry. The representations that appear in the ray operator index are therefore different, for n ≤ 7, from those appearing in the previously computed superconformal index. For 3 ≤ n ≤ 7, we find that the leading term in the index is a character of a minuscule representation of E_n . We also discuss the case n = 8, which presents a unique technical challenge, and remains an open problem.

We investigate a class of supersymmetric quantum mechanical theories (with two supercharges) having tensor-valued degrees of freedom which are dominated by melon diagrams in the large N limit. One motivation was to examine the interplay between supersymmetry and melonic dominance and potential implications for building toy models of holography. We find a definite tension between supersymmetry (with dynamical bosons) and melonic dominance in this class of systems. More specifically, our theories attain a low energy non-supersymmetric conformal fixed point. The origin of supersymmetry breaking lies in the need to regularize bosonic and fermionic degrees of freedom independently. We investigate various aspects of the low energy spectrum and also comment on related examples with different numbers of supercharges. Along the way we also derive some technical results for SL(2, ℝ) wavefunctions for fermionic excitations.

We investigate a charged two-dimensional particle in a homogeneous magnetic field interacting with a periodic array of point obstacles. We show that while Landau levels remain to be infinitely degenerate eigenvalues, between them the system has bands of absolutely continuous spectrum and exhibits thus a transport along the array. We also compute the band functions and the corresponding probability current.