Algebraic Realisation of the Zamolodchikov Metric in Narain Theories

IF 7.8 3区物理与天体物理 Q1 PHYSICS, MULTIDISCIPLINARY

Fortschritte Der Physik-Progress of Physics Pub Date : 2026-04-13 DOI:10.1002/prop.70098

E. H Saidi, R. Sammani

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引用次数: 0

Abstract

We revisit Narain conformal field theories ( ${NCFT}_{2}$ )from an algebraic perspective based on finite dimensional Lie algebras $g$ and representations $R_{g}$ , and show how the root and weight lattices can encode the momenta and subsequently the partition functions of Narain theories. In this framework, we construct a realisation of the Zamolodchikov metric of the moduli space $M_{g}$ in terms of Lie algebraic data, namely, the Cartan matrix $K_{g}$ and its inverse $K_{g}^{- 1}$ . Properties regarding the ensemble averaging of these CFTs and their holographic dual are also derived. Additionally, we discuss possible generalisations to NCFTs having dis-symmetric central charges $(c_{L}, c_{R}) = (s, r)$ with $s > r$ , and highlight further features of the partition function $Z_{g}^{(r, r)}$ .

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Narain理论中Zamolodchikov度规的代数实现

基于有限维李代数g $\mathbf {g}$和表示R g $\mathbf {R}_{\mathbf {g}}$，从代数的角度重新审视了Narain共形场理论（NCFT 2 ${\rm NCFT}_{2}$）。并展示了根格和权格如何编码纳拉因理论的动量和随后的配分函数。在这个框架中，我们构造了模空间M g $\mathcal {M}_{\mathbf {g}}$的Zamolodchikov度规在李代数数据中的实现，即：卡坦矩阵K g ${\rm K}_{\mathbf {g}}$及其逆K g−1 ${\rm K}_{\mathbf {g}}}^{-1}$。本文还推导了这些CFTs及其全息对偶的系综平均性质。此外，我们还讨论了具有非对称中心电荷的NCFTs的可能推广。c R)=(s， R) $(\ mathm {c}_{L},\ mathm {c}_{R})=(\ mathm {s}，\ mathm {r})$ with s>r$ >r$，并强调配分函数Z g (r，r) ${\rm Z}_{\mathbf {g}}^{(r,r)}$。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Fortschritte Der Physik-Progress of Physics 物理-物理：综合

CiteScore

6.70

自引率

7.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The journal Fortschritte der Physik - Progress of Physics is a pure online Journal (since 2013). Fortschritte der Physik - Progress of Physics is devoted to the theoretical and experimental studies of fundamental constituents of matter and their interactions e. g. elementary particle physics, classical and quantum field theory, the theory of gravitation and cosmology, quantum information, thermodynamics and statistics, laser physics and nonlinear dynamics, including chaos and quantum chaos. Generally the papers are review articles with a detailed survey on relevant publications, but original papers of general interest are also published.