相关论文: String bordism and chromatic characteristics

It has been recently conjectured that the spectral determinants of operators associated to mirror curves can be expressed in terms of a generalization of theta functions, called quantum theta functions. In this paper we study the symplectic…

This is an exposition of facts about p-local spectra, p-complete spectra and modules over the p-complete sphere spectrum, including homological criteria for finiteness. Most things are well-known to the experts, with a couple of potential…

We investigate hetrotic string theory on special holonomy manifolds including exceptional holonomy G_2 and Spin(7) manifolds. The gauge symmetry is F_4 in a G_2 manifold compactification, and so(9) in a Spin(7) manifold compactification. We…

Heterotic string theory compactified on a K3 surface times T^2 is believed to be equivalent to type II string theory on a suitable Calabi-Yau threefold. In particular, it must share the same hypermultiplet moduli space. Building on the…

We offer a complete description of $THH(E(2))$ under the assumption that the Johnson-Wilson spectrum $E(2)$ at a chosen odd prime carries an $E_\infty$-structure. We also place $THH(E(2))$ in a cofiber sequence $E(2) \rightarrow…

It is shown that the K-theory of every noetherian base scheme of finite Krull dimension is represented by a strict ring object in the setting of motivic stable homotopy theory. The adjective `strict' is used to distinguish between the type…

We point out that the celebrated Hawking effect of quantum instability of black holes seems to be related to a nonperturbative effect in string theory. Studying quantum dynamics of strings in the gravitational background of black holes we…

We classify modules and rings with some specific properties of their intersection graphs. In particular, we describe rings with infinite intersection graphs containing maximal left ideals of finite degree. This answers a question raised in…

In arXiv:0905.3629 we described a new class of N=2 topological amplitudes that depends both on vector and hypermultiplet moduli. Here we find that this class is actually a particular case of much more general topological amplitudes which…

We describe the ring of modular forms of degree 2 in characteristic 2 using its relation with curves of genus 2.

The $\alpha'$-expansion of string theory provides a rich set of higher-dimension operators, indexed by $\zeta$ values, which can be used to study color-kinematics duality and the double copy. These two powerful properties, actually first…

We apply some methods of homology and K-theory to special classes of branes wrapping homologically nontrivial cycles. We treat the classification of four-geometries in terms of compact stabilizers (by analogy with Thurston's classification…

We use Stirling number identities developed recently in number theory to show that ratios among high energy string scattering amplitudes in the fixed angle regime can be extracted from the Kummer function of the second kind. This result not…

String theory can accommodate black holes with the black hole parameters related to string moduli. It is a well known but remarkable feature that the near horizon geometry of a large class of black holes arising from string theory contains…

Let G be a simple Lie group of real rank one, and S the ideal boundary of the corresponding symmetric space of noncompact type (H^n_R, H^n_C, H^n_H or H^2_O). We show the finiteness of the possible values of the secondary characteristic…

We show that the BRST structure of the topological string is encoded in the ``small'' $N=4$ superconformal algebra, enabling us to obtain, in a non-trivial way, the string theory from hamiltonian reduction of $A(1|1)$. This leads to the…

We extend knot Floer homology to string links in D^{2} \times I and to d-based links in arbitrary three manifolds, without any hypothesis on the null-homology of the components. As for knot Floer homology we obtain a description of the…

We set up foundations of representation theory over $S$, the sphere spectrum, which is the `initial ring' of stable homotopy theory. In particular, we treat $S$-Lie algebras and their representations, characters, $gl_n(S)$-Verma modules and…

Given a Bravais colouring of planar modules $\M_n:=\Z[\xi_n]$, where $\xi_n$ is a primitive $n$th root of unity, two important colour groups arise: the colour symmetry group $H$, which permutes the colours of a given colouring of $\M_n$,…

When $p$ is an odd prime, we prove that the $\mathbb F_p$-cohomology of $\mathrm{BP}\langle n\rangle$ as a module over the Steenrod algebra determines the $p$-local spectrum $\mathrm{BP}\langle n\rangle$. In particular, we prove that the…