On gl（2｜2）（2）k Current Superalgebra and Twisted Conformal Field Theory

Motivated by the recently discovered hidden symmetry of the type IIB Green-Schwarz superstring on certain background, the non-semisimple Kac-Moody twisted superalgebra gl（2｜2）（2）k is investigated by means of the vector coherent state method and boson-fermion realization. The free field realization of the twisted current superalgebra at general level k is constructed. The corresponding Conformai Field Theory （CFT） has zero central charge. According to the classification theory, this CFT is a nonunitary field theory. After projecting out a U（1） factor and an outer automorphism operator, we get the free field representation of psl（2｜2）（2）k, which is the a/gebra of gl（2｜2）（2）k modulo the Z4-outer automorphism, the CFT has central charge -2.

Weak gravity conjecture from conformal field theory:a challenge from hyperscaling violating and Kerr-Newman-AdS black holes

We search for a possible relationship between weak gravity conjecture(WGC)and conformal field theory(CFT)in hyperscaling violating and Kerr-Newman-AdS black holes.We deal with the critical points of the black hole systems using the correlation function introduced in CFT and discuss WGC conditions using the imaginary part of the energy obtained from the critical points and their poles.Under the assumptions z=1,d=1,andθ→0-,we link WGC to hyperscaling violating black holes owing to the existence of rHvalues larger and smaller than one.For the second black hole system,we study the conditions of WGC for Kerr-Newman-AdS black holes using rotation and radius parameters.Then,we show that the conditions of WGC are satisfied when the charged particle near the hyperscaling violating and Kerr-Newman black holes is 1/a with a ratio a/l《1.

Convergence in Conformal Field Theory

Convergence and analytic extension are of fundamental importance in the mathematical construction and study of conformal field theory.The author reviews some main convergence results,conjectures and problems in the construction and study of conformal field theories using the representation theory of vertex operator algebras.He also reviews the related analytic extension results,conjectures and problems.He discusses the convergence and analytic extensions of products of intertwining operators(chiral conformal fields)and of q-traces and pseudo-q-traces of products of intertwining operators.He also discusses the convergence results related to the sewing operation and the determinant line bundle and a higher-genus convergence result.He then explains conjectures and problems on the convergence and analytic extensions in orbifold conformal field theory and in the cohomology theory of vertex operator algebras.

A pedagogical review on solvable irrelevant deformations of 2D quantum field theory

This is a pedagogical review on TT^(-)deformation of two dimensional quantum field theories.It is based on three lectures which the author gave at ITP-CAS in December 2018.This review consists of four parts.The first part is a general introduction to TT^(-)deformation.Special emphasises are put on the deformed classical Lagrangian and the exact solvability of the spectrum.The second part focuses on the torus partition sum of the TT^(-)/JT^(-)deformed conformal field theories and modular invariance/covariance.In the third part,different perspectives of TT^(-)deformation are presented,including its relation to random geometry,2D topological gravity and holography.We summarize more recent developments until January 2021 in the last part.

Boundary States and Correlation Functions of Tricritical Ising Model from Coulomb-Gas Formalism

We consider the minimal conformaJ model describing the tricritical Ising model on the disk and on the upper half plane. Using the coulomb-gas formalism we determine its consistents boundary states as well as its one-point and two-point correlation functions.

Hecke-Langlands Duality and Witten’s Gravitational Moonshine

The purpose of this research is to give a dual description of conformal blocks of d=2 rational CFT (conformal field theory) in terms of Hecke eigenforms and eigensheaves. In particular, partition functions, conformal characters and lattice theta functions may be reconstructed from the action of Hecke operators. This method can be applied to: 1) rings of integers of Galois number fields equipped with the trace (or anti-trace) form;2) root lattices of affine Kac-Moody algebras and WZW-models;3) minimal models of Belavin-Polyakov-Zamolodchikov and related d=2 spin-chain/lattice models;4) vertex algebras of Leech and Niemeier lattices and others. We also use the original Witten’s idea to construct the 3-dimensional quantum gravity as the AdS/CFT-dual of c=24 Monster vertex algebra of Frenkel-Lepowsky- Meurman. Concerning the geometric Langlands duality, we use results of Beilinson-Drinfeld, Frenkel-Ben-Zvi, Gukov-Kapustin-Witten and many others (cf. references). The main new result in this paper is the construction of number-theoretical lattice vertex superalgebras in Section 5 and applications to conformal field theories and quantum gravity.

Relic Entropy Growth and Initial Big Bang Conditions, as a Subset of Quantum Information

This paper shows how increased entropy values from an initially low big bang level can be measured experimentally by counting relic gravitons. Furthermore the physical mechanism of this entropy increase is explained via analogies with early-universe phase transitions. The role of Ng’s revised infinite quantum statistics in the physics of gravitational wave detection is acknowledged. Ng’s infinite quantum statistics can be used to show that is a starting point to the increasing net universe cosmological entropy. Finally, in a nod to similarities with zero point energy (ZPE) analysis, it is important to note that the resulting in fact is much lower, allowing for evaluating initial graviton production as an emergent field phenomena, which may be similar to how ZPE states can be used to extract energy from a vacuum if entropy is not maximized. The rapid increase in entropy so alluded to without near sudden increases to 1088 may be enough to allow successful modeling of relic graviton production for entropy in a manner similar to zero point energy (ZPE) energy extraction from a vacuum state. This entropy count is akin to quantum information models used to tell how much “information” may be stored in initial conditions, and transferred from a prior to the present

Finite dimensional irreducible representations of Lie superalgebra D(2,1;α)

This paper focuses on the finite dimensional irreducible representations of Lie superalgebra D(2,1;α).We explicitly construct the finite dimensional representations of the superalgebra D(2,1;α)by using the shift operator and differential operator representations.Unlike ordinary Lie algebra representation,there are typical and atypical representations for most superalgebras.Therefore,its typical and atypical representation conditions are also given.Our results are expected to be useful for the construction of primary fields of the corresponding current superalgebra of D(2,1;α).

Note on non-vacuum conformal family contributions to Rényi entropy in two-dimensional CFT

We calculate the contributions of a general non-vacuum conformal family to R′enyi entropy in twodimensional conformal field theory（CFT）. The primary operator of the conformal family can be either non-chiral or chiral, and we denote its scaling dimension by ？. For the case of two short intervals on a complex plane, we expand the R′enyi mutual information by the cross ratio x to order x^（2△＋2）. For the case of one interval on a torus with low temperature, we expand the R′enyi entropy by q = exp（-2πβ/L）, with β being the inverse temperature and L being the spatial period, to order q^（△＋2）. To make the result meaningful, we require that the scaling dimension ？ cannot be too small. For two intervals on a complex plane we need △ 〉 1, and for one interval on a torus we need △ 〉 2.We work in the small Newton constant limit on the gravity side and so a large central charge limit on the CFT side,and find matches of gravity and CFT results.

General Rotating Black Hole with Four Charges and Liouville Theory

By considering the dual Liouville theory emerging in the near-horizon limit, we study the thermodynamics of general rotating black hole with four charges in four dimensions. Both the black hole entropy and temperature are found to agree with the gravitational expectations. The relations between the new Liouville formalism and the anomaly approach are also discussed.

Genus two correlation functions in CFTs with TT deformation

Since the definition of TT deformation in the curved Riemann surface is obstructive in the literature,we propose a way to do the deformation in the genus two Riemann surfaces by sewing prescription.We construct the correlation functions of conformal field theories(CFTs)on genus two Riemann surfaces with the TT deformation in terms of the perturbative CFT approach.Thanks to sewing construction to form higher genus Riemann surfaces from lower genus ones and conformal symmetry,we systematically obtain the first-order TT correction to the genus two correlation functions in the TT deformed CFTs,e.g.,partition function and one/higher-point correlation functions.

Introduction to holographic superconductor models

In the last years it has been shown that some properties of strongly coupled superconductors can be potentially described by classical general relativity living in one higher dimension,which is known as holographic superconductors.This paper gives a quick and introductory overview of some holographic superconductor models with s-wave,p-wave and d-wave orders in the literature from point of view of bottom-up,and summarizes some basic properties of these holographic models in various regimes.The competition and coexistence of these superconductivity orders are also studied in these superconductor models.

Note on higher-point correlation functions of the TT or JT deformed CFTs

We investigate generic n-point correlation functions of conformal field theories(CFTs),with TT and JT deformations,in terms of the perturbative CFT approach.We systematically obtain the first order correction to the generic correlation functions of CFTs with TT or JT deformation.We compute the out of time ordered correlation function(OTOC)in the Ising model with TT or Jdeformation,which confirms that these deformations do not change the integrable property up to the first order level.

N-cluster correlations in four-and five-dimensional percolation

We study N-cluster correlation functions in four-and five-dimensional(4D)and 5D)bond percolation by extensive Monte Carlo simulation.We reformulate the transfer Monte Carlo algorithm for percolation[Phys.Reu.E 72,016126(2005)]using the disjoint-set data structure,and simulate a cylindrical geometry Ld^-1×∞,with the linear size up to L=512 for 4D and 128 for 5D.We determine with 1 high precision all possible N-cluster exponents,for N=2 and 3,and the universal amplitude for a logarithmic correlation function.From the symmetric correlator with N=2,we obtain the correlation-length critical exponent as 1/v=1.4610(12)for 4D and 1/v=1.737(2)for 5D,significantly improving over the existing results.Estimates for the other exponents and the universal logarithmic amplitude have not been reported before to our knowledge.Our work demonstrates the validity of logarithmic conformal field theory and adds to the growing knowledge for high-dimensional percolation.

Harrison Metrics for the Schwarzschild Black Hole

Based on the hidden conformed symmetry, some authors have proposed a Harrison metric for the Schwarzschild black hole. We give a procedure which can generate a family of Harrison metrics starting from a general set of SL（2, R） vector fields. By analogy with the subtracted geometry of the Kerr black hole, we find a new Harrison metric for the Schwaxzschild case. its conformal generators axe also investigated using the Killing equations in the near-horizon limit.