Abstract Duality refers to two equivalent descriptions of the same theory from different points of view. Recently there has been tremendous progress in formulating and understanding possible dualities of quantum many body theories in 2 + 1 -spacetime dimensions. Of particular interest are dualities that describe conformally invariant quantum field theories in ( 2 + 1 ) d . These arise as descriptions of quantum critical points in condensed matter physics. The appreciation of the possible dual descriptions of such theories has greatly enhanced our understanding of some challenging questions about such quantum critical points. Perhaps surprisingly the same dualities also underlie recent progress in our understanding of other problems such as the half-filled Landau level and correlated surface states of topological insulators. Here we provide a pedagogical review of these recent developments from a point of view geared toward condensed matter physics.

中文翻译：

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(2+1)d 量子临界点之间的对偶性

摘要 二元性是指从不同的角度对同一理论的两种等价描述。最近，在制定和理解 2 + 1 时空维度中量子多体理论的可能对偶性方面取得了巨大进展。特别感兴趣的是描述 (2+1)d 中的共形不变量子场论的对偶性。这些是作为凝聚态物理学中量子临界点的描述而出现的。对此类理论可能的双重描述的理解极大地增强了我们对有关此类量子临界点的一些具有挑战性的问题的理解。也许令人惊讶的是，相同的二元性也是我们对其他问题（例如半填充朗道能级和拓扑绝缘体的相关表面状态）的理解的最新进展的基础。