scholarly journals CONFORMAL SYMMETRY OF SUPERSTRINGS ON AdS3 × S3 × T4 AND D1/D5 System

2002 ◽  
Vol 17 (37) ◽  
pp. 2477-2485 ◽  
Author(s):  
ABBAS ALI
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Conformal Symmetry ◽  
Space Time ◽  
Superconformal Algebra ◽  
Superconformal Symmetry ◽  
Conformal Field ◽  
Time Symmetry

Conformal field theory of the D1/D5 system and superstrings on AdS3 × S3 × T4 is studied with particular attention to the worldsheet fields corresponding to the T4 part. A solution to the space–time N = 4 superconformal symmetry doubling and other problems is proposed. It is argued that the relevant space–time symmetry should be based on the middle N = 4 superconformal algebra. It is discussed as to why this superconformal structure has been missed so far.

scholarly journals NONCOMMUTATIVE CONFORMAL FIELD THEORY IN THE TWIST-DEFORMED CONTEXT

2008 ◽  
Vol 23 (39) ◽  
pp. 3307-3315 ◽  
Author(s):  
FEDELE LIZZI ◽  
PATRIZIA VITALE
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Noncommutative Geometry ◽  
Conformal Symmetry ◽  
Two Dimensional ◽  
Moyal Product ◽  
Conformal Field ◽  
Noncommutative Plane

We discuss conformal symmetry on the two-dimensional noncommutative plane equipped with Moyal product in the twist deformed context. We show that the consistent use of the twist procedure leads to results which are free from ambiguities. This lends support to the importance of the use of twist symmetries in noncommutative geometry.

scholarly journals Simple space-time symmetries: Generalizing conformal field theory

2007 ◽  
Vol 48 (5) ◽  
pp. 052304 ◽  
Author(s):  
Gerhard Mack ◽  
Mathias de Riese
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Space Time ◽  
Conformal Field

ON THE INTERPOLATING SOLUTIONS OF STRING IN DIFFERENT BACKGROUNDS

1992 ◽  
Vol 07 (15) ◽  
pp. 1361-1366 ◽  
Author(s):  
SUDIPTA MUKHERJI
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
String Theory ◽  
Central Charge ◽  
Space Time ◽  
Time Dependent ◽  
Target Space ◽  
Conformal Field ◽  
Β Function ◽  
Time Dependent Solution

We analyze the β-function equations for string theory in the case when the target space has one space-like (or time-like) direction and the rest is some conformal field theory (CFT) with appropriate central charge and has one nearly marginal operator. We show there always exists a space-(time) dependent solution which interpolates between the original background and the background where CFT is replaced by a new conformal field theory, obtained by perturbing CPT by the nearly marginal operator.

scholarly journals Effects of non-conformal boundary on entanglement entropy

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Andrew Loveridge
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Conformal Field Theory ◽  
Boundary Conditions ◽  
Mixed Boundary ◽  
Conformal Symmetry ◽  
Entanglement Entropy ◽  
Mixed Boundary Conditions ◽  
De Sitter ◽  
Conformal Field

Abstract Spacetime boundaries with canonical Neuman or Dirichlet conditions preserve conformal invarience, but “mixed” boundary conditions which interpolate linearly between them can break conformal symmetry and generate interesting Renormalization Group flows even when a theory is free, providing soluble models with nontrivial scale dependence. We compute the (Rindler) entanglement entropy for a free scalar field with mixed boundary conditions in half Minkowski space and in Anti-de Sitter space. In the latter case we also compute an additional geometric contribution, which according to a recent proposal then collectively give the 1/N corrections to the entanglement entropy of the conformal field theory dual. We obtain some perturbatively exact results in both cases which illustrate monotonic interpolation between ultraviolet and infrared fixed points. This is consistent with recent work on the irreversibility of renormalization group, allowing some assessment of the aforementioned proposal for holographic entanglement entropy and illustrating the generalization of the g-theorem for boundary conformal field theory.

scholarly journals 4-point function from conformally coupled scalar in AdS6

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Jae-Hyuk Oh
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Correlation Functions ◽  
Ward Identity ◽  
Conformal Symmetry ◽  
Classical Solutions ◽  
Point Function ◽  
Conformal Theory ◽  
Conformal Field ◽  
Linear Limit

Abstract We explore conformally coupled scalar theory in AdS6 extensively and their classical solutions by employing power expansion order by order in its self-interaction coupling λ. We describe how we get the classical solutions by diagrammatic ways which show general rules constructing the classical solutions. We study holographic correlation functions of scalar operator deformations to a certain 5-dimensional conformal field theory where the operators share the same scaling dimension ∆ = 3, from the classical solutions. We do not assume any specific form of the micro Lagrangian density of the 5-dimensional conformal field theory. For our solutions, we choose a scheme where we remove co-linear divergences of momenta along the AdS boundary directions which frequently appear in the classical solutions. This shows clearly that the holographic correlation functions are free from the co-linear divergences. It turns out that this theory provides correct conformal 2- and 3- point functions of the ∆ = 3 scalar operators as expected in previous literature. It makes sense since 2- and 3- point functions are determined by global conformal symmetry not being dependent on the details of the conformal theory. We also get 4-point function from this holographic model. In fact, it turns out that the 4-point correlation function is not conformal because it does not satisfy the special conformal Ward identity although it does dilation Ward identity and respect SO(5) rotation symmetry. However, in the co-linear limit that all the external momenta are in a same direction, the 4-point function is conformal which means that it satisfy the special conformal Ward identity. We inspect holographic n-point functions of this theory which can be obtained by employing a certain Feynman-like rule. This rule is a construction of n-point function by connecting l-point functions each other where l < n. In the co-linear limit, these n-point functions reproduce the conformal n-point functions of ∆ = 3 scalar operators in d = 5 Euclidean space addressed in arXiv:2001.05379.

scholarly journals Defect conformal blocks from Appell functions

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Ilija Burić ◽  
Volker Schomerus
Keyword(s):  
Field Theory ◽  
Correlation Function ◽  
Conformal Field Theory ◽  
Hypergeometric Functions ◽  
Conformal Symmetry ◽  
Scalar Fields ◽  
Conformal Blocks ◽  
Conformal Field ◽  
Additional Defect ◽  
Appell Functions

Abstract We develop a group theoretical formalism to study correlation functions in defect conformal field theory, with multiple insertions of bulk and defect fields. This formalism is applied to construct the defect conformal blocks for three-point functions of scalar fields. Starting from a configuration with one bulk and one defect field, for which the correlation function is determined by conformal symmetry, we explore two possibilities, adding either one additional defect or bulk field. In both cases it is possible to express the blocks in terms of classical hypergeometric functions, though the case of two bulk and one defect field requires Appell’s function F4.

A twistor conformal field theory for four space-time dimensions

1989 ◽  
Vol 216 (1-2) ◽  
pp. 48-52 ◽  
Author(s):  
A.P. Hodges ◽  
R. Penrose ◽  
M.A. Singer
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Space Time ◽  
Conformal Field

scholarly journals On Galilean conformal bootstrap

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Bin Chen ◽  
Peng-xiang Hao ◽  
Reiko Liu ◽  
Zhe-fei Yu
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Inversion Formula ◽  
Conformal Symmetry ◽  
Taylor Series Expansion ◽  
Point Function ◽  
Conformal Field ◽  
Conformal Bootstrap ◽  
Free Theory ◽  
Exact Agreement

Abstract In this work, we develop conformal bootstrap for Galilean conformal field theory (GCFT). In a GCFT, the Hilbert space could be decomposed into quasiprimary states and its global descendants. Different from the usual conformal field theory, the quasiprimary states in a GCFT constitute multiplets, which are block-diagonized under the Galilean boost operator. More importantly the multiplets include the states of negative norms, indicating the theory is not unitary. We compute global blocks of the multiplets, and discuss the expansion of four-point functions in terms of the global blocks of the multiplets. Furthermore we do the harmonic analysis for the Galilean conformal symmetry and obtain an inversion formula. As the first step to apply the Galilean conformal bootstrap, we construct generalized Galilean free theory (GGFT) explicitly. We read the data of GGFT by using Taylor series expansion of four-point function and the inversion formula independently, and find exact agreement. We discuss some novel features in the Galilean conformal bootstrap, due to the non-semisimpleness of the Galilean conformal algebra and the non-unitarity of the GCFTs.

scholarly journals CONFORMAL FIELD THEORY ON R × S3 FROM QUANTIZED GRAVITY

2009 ◽  
Vol 24 (16n17) ◽  
pp. 3073-3110 ◽  
Author(s):  
KEN-JI HAMADA
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Conformal Transformation ◽  
Conformal Symmetry ◽  
Conformal Factor ◽  
Combined System ◽  
Four Dimensions ◽  
Gravitational Fields ◽  
Conformal Field ◽  
Gauge Fixing

Conformal algebra on R × S3 derived from quantized gravitational fields is examined. The model we study is a renormalizable quantum theory of gravity in four dimensions described by a combined system of the Weyl action for the traceless tensor mode and the induced Wess–Zumino action managing nonperturbative dynamics of the conformal factor in the metric field. It is shown that the residual diffeomorphism invariance in the radiation+ gauge is equal to the conformal symmetry, and the conformal transformation preserving the gauge-fixing condition that forms a closed algebra quantum mechanically is given by a combination of naive conformal transformation and a certain field-dependent gauge transformation. The unitarity issue of gravity is discussed in the context of conformal field theory. We construct physical states by solving the conformal invariance condition and calculate their scaling dimensions. It is shown that the conformal symmetry mixes the positive-metric and the negative-metric modes and thus the negative-metric mode does not appear independently as a gauge invariant state at all.

scholarly journals Emergent Replica Conformal Symmetry in Non-Hermitian SYK2 Chains

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 579
Author(s):  
Pengfei Zhang ◽  
Shao-Kai Jian ◽  
Chunxiao Liu ◽  
Xiao Chen
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Conformal Symmetry ◽  
Entanglement Entropy ◽  
Vortex Pair ◽  
Free Fermion ◽  
Conformal Field ◽  
Point Solution ◽  
Critical Phases ◽  
Goldstone Modes

Recently, the steady states of non-unitary free fermion dynamics are found to exhibit novel critical phases with power-law squared correlations and a logarithmic subsystem entanglement. In this work, we theoretically understand the underlying physics by constructing solvable static/Brownian quadratic Sachdev-Ye-Kitaev chains with non-Hermitian dynamics. We find the action of the replicated system generally shows (one or infinite copies of) O(2)×O(2) symmetries, which is broken to O(2) by the saddle-point solution. This leads to an emergent conformal field theory of the Goldstone modes. We derive the effective action and obtain the universal critical behaviors of squared correlators. Furthermore, the entanglement entropy of a subsystem A with length LA corresponds to the energy of the half-vortex pair S∼ρslog⁡LA, where ρs is the total stiffness of the Goldstone modes. We also discuss special limits with more than one branch of Goldstone modes and comment on interaction effects.

Sign in / Sign up

Export Citation Format

Share Document