scholarly journals Holographic Rényi entropy for two-dimensional N = 1 , 1 $$ \mathcal{N}=\left(1,\;1\right) $$ superconformal field theory

2015 ◽  
Vol 2015 (12) ◽  
pp. 1-19 ◽  
Author(s):  
Jia-ju Zhang
Keyword(s):  
Field Theory ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Two Dimensional ◽  
Superconformal Field Theory

scholarly journals Excited state Rényi entropy and subsystem distance in two-dimensional non-compact bosonic theory. Part II. Multi-particle states

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Jiaju Zhang ◽  
M. A. Rajabpour
Keyword(s):  
Field Theory ◽  
Excited State ◽  
Excited States ◽  
Short Interval ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Two Dimensional ◽  
Bosonic Field ◽  
Conformal Field ◽  
Harmonic Chain

Abstract We study the excited state Rényi entropy and subsystem Schatten distance in the two-dimensional free massless non-compact bosonic field theory, which is a conformal field theory. The discretization of the free non-compact bosonic theory gives the harmonic chain with local couplings. We consider the field theory excited states that correspond to the harmonic chain states with excitations of more than one quasiparticle, which we call multi-particle states. This extends the previous work by the same authors to more general excited states. In the field theory we obtain the exact Rényi entropy and subsystem Schatten distance for several low-lying states. We obtain short interval expansion of the Rényi entropy and subsystem Schatten distance for general excited states, which display different universal scaling behaviors in the gapless and extremely gapped limits of the non-compact bosonic theory. In the locally coupled harmonic chain we calculate numerically the excited state Rényi entropy and subsystem Schatten distance using the wave function method. We find excellent matches of the analytical results in the field theory and numerical results in the gapless limit of the harmonic chain. We also make some preliminary investigations of the Rényi entropy and the subsystem Schatten distance in the extremely gapped limit of the harmonic chain.

scholarly journals Excited state Rényi entropy and subsystem distance in two-dimensional non-compact bosonic theory. Part I. Single-particle states

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Jiaju Zhang ◽  
M.A. Rajabpour
Keyword(s):  
Excited States ◽  
Single Particle ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Large Momentum ◽  
Particle State ◽  
Two Dimensional ◽  
Universal Form ◽  
Conformal Field ◽  
Harmonic Chain

Abstract We investigate the Rényi entropy of the excited states produced by the current and its derivatives in the two-dimensional free massless non-compact bosonic theory, which is a two-dimensional conformal field theory. We also study the subsystem Schatten distance between these states. The two-dimensional free massless non-compact bosonic theory is the continuum limit of the finite periodic gapless harmonic chains with the local interactions. We identify the excited states produced by current and its derivatives in the massless bosonic theory as the single-particle excited states in the gapless harmonic chain. We calculate analytically the second Rényi entropy and the second Schatten distance in the massless bosonic theory. We then use the wave functions of the excited states and calculate the second Rényi entropy and the second Schatten distance in the gapless limit of the harmonic chain, which match perfectly with the analytical results in the massless bosonic theory. We verify that in the large momentum limit the single-particle state Rényi entropy takes a universal form. We also show that in the limit of large momenta and large momentum difference the subsystem Schatten distance takes a universal form but it is replaced by a new corrected form when the momentum difference is small. Finally we also comment on the mutual Rényi entropy of two disjoint intervals in the excited states of the two-dimensional free non-compact bosonic theory.

scholarly journals Infrared Electric Image Thresholding Using Two-Dimensional Fuzzy Renyi Entropy

2011 ◽  
Vol 12 ◽  
pp. 411-419 ◽  
Author(s):  
Songhai Fan ◽  
Shuhong Yang ◽  
Pu He ◽  
Hongyu Nie
Keyword(s):  
Renyi Entropy ◽  
Rényi Entropy ◽  
Two Dimensional ◽  
Image Thresholding ◽  
Electric Image

scholarly journals The Notion of N=1 Supergeometric Vertex Operator Superalgebra and the Isomorphism Theorem

2003 ◽  
Vol 05 (04) ◽  
pp. 481-567 ◽  
Author(s):  
Katrina Barron
Keyword(s):  
Field Theory ◽  
Vertex Operator ◽  
Isomorphism Theorem ◽  
Two Dimensional ◽  
Genus Zero ◽  
Superconformal Field Theory ◽  
Vertex Operator Superalgebra

We introduce the notion of N=1supergeometric vertex operator superalgebra motivated by the geometry underlying genus-zero, two-dimensional, holomorphic N=1 superconformal field theory. We then show, assuming the convergence of certain projective factors, that the category of such objects is isomorphic to the category of N=1 Neveu–Schwarz vertex operator superalgebras.

scholarly journals Non-compact superconformal field theory and mock modular forms

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Yuji Sugawara
Keyword(s):  
Field Theory ◽  
High Energy Phys ◽  
Modular Forms ◽  
High Energy ◽  
Field Theories ◽  
Two Dimensional ◽  
Superconformal Field Theories ◽  
Superconformal Field Theory ◽  
Mock Modular Forms ◽  
Mathematical Literature

Abstract One of interesting issues in two-dimensional superconformal field theories is the existence of anomalous modular transformation properties appearing in some non-compact superconformal models, corresponding to the “mock modularity” in mathematical literature. I review a series of my studies on this issue in collaboration with T. Eguchi, mainly focusing on T. Eguchi and Y. Sugawara, J. High Energy Phys. 1103, 107 (2011); J. High Energy Phys. 1411, 156 (2014); and Prog. Theor. Exp. Phys. 2016, 063B02 (2016).

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