ADVANCES IN THEORETICAL AND MATHEMATICAL PHYSICS 是国际出版社的双月刊，发表关于理论物理和数学相互作用的所有领域的论文。

Advances in Theoretical and Mathematical Physics is a bimonthly journal published by an international publisher, focusing on research papers in all areas of the interaction between theoretical physics and mathematics.

《Advances in Theoretical and Mathematical Physics》是国际出版社出版的双月刊，专注于发表理论物理与数学交叉领域的研究论文。

Advances in Theoretical and Mathematical Physics

Let M be a complete Einstein manifold of negative curvature, and assume that (as in the AdS/CFT correspondence) it has a Penrose compactification with a conformal boundary TV of positive scalar curvature.We show that under these conditions, jy n (M;Z) = 0 and in particular N must be connected.These results resolve some puzzles concerning the AdS/CFT correspondence.

Edward Witten

S.-T. Yau

Connectedness of the boundary in the $\mathrm{AdS}$/$\mathrm{CFT}$ correspondence

$\mathrm{AdS}$/$\mathrm{CFT}$对应中边界的连通性

We derive two geometric approaches to categorification of quantum invariants of links associated to an arbitrary compact simple Lie group $^L{G}$. In part I, we describe the first approach, based on an equivariant derived category of coherent sheaves on ${\cal X}$, the moduli space of singular $G$-monopoles, where $G$ is related to $^LG$ by Langlands duality. In part II, we describe the second approach, based on the derived category of a Fukaya-Seidel category of a Calabi-Yau $Y$ with potential $W$. The two approaches are related by a version of mirror symmetry, which plays a crucial role in the story. In part III, we explain the string theory origin of these results, and the relation to an approach due to Witten.

Mina Aganagic

Knot categorification from mirror symmetry part I: Coherent sheaves

镜像对称与纽结分类提升 第一部分：凝聚层

We study the notion of a causal time-evolution of a conserved nonlocal physical quantity in a globally hyperbolic spacetime $\mathcal{M}$. The role of the `global time' is played by a chosen Cauchy temporal function $\mathcal{T}$, whereas the instantaneous configurations of the nonlocal quantity are modeled by probability measures $\mu_t$ supported on the corresponding time slices $\mathcal{T}^{-1}(t)$. We show that the causality of such an evolution can be expressed in three equivalent ways: (i) via the causal precedence relation $\preceq$ extended to probability measures, (ii) with the help of a probability measure $\sigma$ on the space of future-directed continuous causal curves endowed with the compact-open topology and (iii) through a causal vector field $X$ of $L^2_{\textrm{loc}}$-regularity, with which the map $t \mapsto \mu_t$ satisfies the continuity equation in the distributional sense. In the course of the proof we find that the compact-open topology is sensitive to the differential properties of the causal curves, being equal to a topology induced from a suitable $H^1_{\textrm{loc}}$-Sobolev space. This enables us to construct $X$ as a vector field in a sense `tangent' to $\sigma$. In addition, we discuss the general covariance of descriptions (i)-(iii), unraveling the geometrical, observer-independent notions behind them.

Tomasz Miller

Causal evolution of probability measures and continuity equation

概率测度的因果演化与连续性方程

Amir Babak Aazami

Obstructions to distinguished Riemannian metrics via Lorentzian geometry

通过洛伦兹几何阻碍的特殊黎曼度量

Sergio Cecotti

Fuchsian ODEs as Seiberg dualities

富克斯型常微分方程作为塞伯格对偶性

Carlo Alberto Cremonini

The geometry of picture changing operators

图像改变算子的几何学

Nikita Sopenko

Chiral topologically ordered states on a lattice from vertex operator algebra

格点上的手性拓扑有序态源自顶点算子代数

Yusuke Kimura

Jacobian Calabi-Yau $3$-fold and charge completeness in six-dimensional theory

雅可比卡拉比-丘 $3$ 维流形与六维理论中的电荷完备性

Abbreviation	Adv. Theor. Math. Phys.
Journal Impact	1.06
Quartiles(Global)	PHYSICS, PARTICLES & FIELDS(Q4)

ISSN	1095-0753, 1095-0761
h-index	81

Publication Information	Publisher: International Press, Inc.，Publishing cycle: ，Journal Type: journal，Open Access Journals: No
Basic data	Year of publication: 1997，Proportion of original research papers: ，Self Citation Rate:， Gold OA Rate:

Advances in Theoretical and Mathematical Physics

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Connectedness of the boundary in the $\mathrm{AdS}$/$\mathrm{CFT}$ correspondence

Knot categorification from mirror symmetry part I: Coherent sheaves

Causal evolution of probability measures and continuity equation

Obstructions to distinguished Riemannian metrics via Lorentzian geometry

Fuchsian ODEs as Seiberg dualities

Knot categorification from mirror symmetry part I: Coherent sheaves

Causal evolution of probability measures and continuity equation

The geometry of picture changing operators

Chiral topologically ordered states on a lattice from vertex operator algebra

Jacobian Calabi-Yau $3$-fold and charge completeness in six-dimensional theory