State dependence of Krylov complexity in 2d CFTs

被引:21
|
作者
Kundu, Arnab [1 ]
Malvimat, Vinay [1 ,2 ]
Sinha, Ritam [3 ]
机构
[1] Homi Bhaba Natl Inst HBNI, Saha Inst Nucl Phys, Theory Div, 1-AF Bidhannagar, Kolkata 700064, India
[2] Asia Pacific Ctr Theoret Phys, 77 Cheongam Ro, Pohang Si 37673, Gyeongsangbuk D, South Korea
[3] Kings Coll London, Dept Math, London WC2R 2LS, England
基金
新加坡国家研究基金会;
关键词
AdS-CFT Correspondence; Gauge-Gravity Correspondence;
D O I
10.1007/JHEP09(2023)011
中图分类号
O412 [相对论、场论]; O572.2 [粒子物理学];
学科分类号
摘要
We compute the Krylov Complexity of a light operator O-L in an eigenstate of a 2d CFT at large central charge c. The eigenstate corresponds to a primary operator O-H under the state-operator correspondence. We observe that the behaviour of K-complexity is different (either bounded or exponential) depending on whether the scaling dimension of OH is below or above the critical dimension h(H) = c/24, marked by the 1st order Hawking-Page phase transition point in the dual AdS(3) geometry. Based on this feature, we hypothesize that the notions of operator growth and K-complexity for primary operators in 2d CFTs are closely related to the underlying entanglement structure of the state in which they are computed, thereby demonstrating explicitly their state-dependent nature. To provide further evidence for our hypothesis, we perform an analogous computation of K-complexity in a model of free massless scalar field theory in 2d, and in the integrable 2d Ising CFT, where there is no such transition in the spectrum of states.
引用
收藏
页数:24
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