Communications in Mathematical Physics最新文献

We study the representations of some simple affine vertex algebras at non-admissible level arising from rank one 4D SCFTs. In particular, we classify the irreducible highest weight modules of (L_{-2}(G_2)) and (L_{-2}(B_3)). It is known by the works of Adamović and Perše that these vertex algebras can be conformally embedded into (L_{-2}(D_4)). We also compute the associated variety of (L_{-2}(G_2)), and show that it is the orbifold of the associated variety of (L_{-2}(D_4)) by the symmetric group of degree 3 which is the Dynkin diagram automorphism group of (D_4). This provides a new interesting example of associated variety satisfying a number of conjectures in the context of orbifold vertex algebras.

We develop representation theoretic techniques to construct three dimensional non-semisimple topological quantum field theories which model homologically truncated topological B-twists of abelian Gaiotto–Witten theory with linear matter. Our constructions are based on relative modular structures on the category of weight modules over an unrolled quantization of a Lie superalgebra. The Lie superalgebra, originally defined by Gaiotto and Witten, is associated to a complex symplectic representation of a metric abelian Lie algebra. The physical theories we model admit alternative realizations as Chern–Simons–Rozansky–Witten theories and supergroup Chern–Simons theories and include as particular examples global forms of (mathfrak {gl}(1 vert 1))-Chern–Simons theory and toral Chern–Simons theory. Fundamental to our approach is the systematic incorporation of non-genuine line operators which source flat connections for the topological flavour symmetry of the theory.

By the Aharonov–Casher theorem, the Pauli operator P has no zero eigenvalue when the normalized magnetic flux (alpha ) satisfies (|alpha |<1), but it does have a zero energy resonance. We prove that in this case a Lieb–Thirring inequality for the (gamma )-th moment of the eigenvalues of (P+V) is valid under the optimal restrictions (gamma ge |alpha |) and (gamma >0). Besides the usual semiclassical integral, the right side of our inequality involves an integral where the zero energy resonance state appears explicitly. Our inequality improves earlier works that were restricted to moments of order (gamma ge 1).

The study of first passage percolation (FPP) for the random interlacements model has been initiated in Andres and Prévost (Ann Appl Probab 34(2):1846–1895), where it is shown that on (mathbb {Z}^d), (dge 3), the FPP distance is comparable to the graph distance with high probability. In this article, we give an asymptotically sharp lower bound on this last probability, which additionally holds on a large class of transient graphs with polynomial volume growth and polynomial decay of the Green function. When considering the interlacement set in the low-intensity regime, the previous bound is in fact valid throughout the near-critical phase. In low dimension, we also present two applications of this FPP result: sharp large deviation bounds on local uniqueness of random interlacements, and on the capacity of a random walk in a ball.

The projective variety of square-zero elements in the six-dimensional minimal supersymmetry algebra is isomorphic to (mathbb {P}^1 times mathbb {P}^3). We use this fact, together with the pure spinor superfield formalism, to study supermultiplets in six dimensions, starting from vector bundles on projective spaces. We classify all multiplets whose derived invariants for the supertranslation algebra form a line bundle over the nilpotence variety; one can think of such multiplets as being those whose holomorphic twists have rank one over Dolbeault forms on spacetime. In addition, we explicitly construct multiplets associated to natural higher-rank equivariant vector bundles, including the tangent and normal bundles as well as their duals. Among the multiplets constructed are the vector multiplet and hypermultiplet, the family of ({mathcal {O}}(n))-multiplets, and the supergravity and gravitino multiplets. Along the way, we tackle various theoretical problems within the pure spinor superfield formalism. In particular, we give some general discussion about the relation of the projective nilpotence variety to multiplets and prove general results on short exact sequences and dualities of sheaves in the context of the pure spinor superfield formalism.

Using the notion of magnetic curvature recently introduced by the first author, we extend E. Hopf’s theorem to the setting of magnetic systems. Namely, we prove that if the magnetic flow on the s-sphere bundle is without conjugate points, then the total magnetic curvature is non-positive, and vanishes if and only if the magnetic system is magnetically flat. We then prove that magnetic flatness is a rigid condition, in the sense that it only occurs when either the magnetic form is trivial and the metric is flat, or when the magnetic system is Kähler, the metric has constant negative sectional holomorphic curvature, and s equals the Mañé critical value.

We construct a non-chiral conformal field theory (CFT) on the torus that accommodates a second quantization of the elliptic Calogero–Sutherland (eCS) model. We show that the CFT operator that provides this second quantization defines, at the same time, a quantum version of a soliton equation called the non-chiral intermediate long-wave (ncILW) equation. We also show that this CFT operator is a second quantization of a generalized eCS model which can describe arbitrary numbers of four different kinds of particles; we propose that these particles can be identified with solitons of the quantum ncILW equation.

We define a new ‘potential-weighted connective constant’ that measures the effective strength of a repulsive pair potential of a Gibbs point process modulated by the geometry of the underlying space. We then show that this definition leads to improved bounds for Gibbs uniqueness for all non-trivial repulsive pair potentials on ({mathbb {R}}^d) and other metric measure spaces. We do this by constructing a tree-branching collection of densities associated to the point process that captures the interplay between the potential and the geometry of the space. When the activity is small as a function of the potential-weighted connective constant this object exhibits an infinite-volume uniqueness property. On the other hand, we show that our uniqueness bound can be tight for certain spaces: the same infinite-volume object exhibits non-uniqueness for activities above our bound in the case when the underlying space has the geometry of a tree.

In this paper, we study rigidity aspects of Penrose’s singularity theorem. Specifically, we aim to answer the following question: if a spacetime satisfies the hypotheses of Penrose’s singularity theorem except with weakly trapped surfaces instead of trapped surfaces, then what can be said about the global spacetime structure if the spacetime is null geodesically complete? In this setting, we show that we obtain a foliation of MOTS which generate totally geodesic null hypersurfaces. Depending on our starting assumptions, we obtain either local or global rigidity results. We apply our arguments to cosmological spacetimes (i.e., spacetimes with compact Cauchy surfaces) and scenarios involving topological censorship.

In this paper, we count the number of Pollicott–Ruelle resonances for open hyperbolic systems and Axiom A flows. In particular, we prove polynomial upper bounds and sublinear lower bounds on the number of resonances with modulus less than r in strips for open hyperbolic systems and Axiom A flows with a transversality condition.