LINEAR GRAVITONS FROM STRINGS

1988 ◽  
Vol 03 (09) ◽  
pp. 917-928 ◽  
Author(s):  
JENNIE H. TRASCHEN
Keyword(s):  
Gauge Invariance ◽  
Sigma Model ◽  
Equations Of Motion ◽  
Vertex Operators ◽  
Polarization Tensor ◽  
Conformal Field Theories ◽  
Conformally Invariant ◽  
Conformal Field ◽  
Stress Energy ◽  
Model Equations

Linear gravitons and spin-two gauge invariance appear in several places in string theories. The purpose of this note is to clarify the connection between gravitons which are emitted by vertex operators in conformal field theories and those which appear in conformally invariant sigma models, and to compare the associated gauge invariances. The polarization tensor and scalar field of a graviton-dilaton vertex are shown to obey equations of motion which are identical to the sigma model equations of motion if, and only if, the trace of the polarization tensor is massless. The gauge invariance of this vertex is a restricted version of the normal spin-two gauge invariance, but is seen to be sufficient to imply conservation of spacetime stress energy of the string.

scholarly journals The conformal anomaly action to fourth order (4T) in $$d=4$$ in momentum space

2021 ◽  
Vol 81 (8) ◽  
Author(s):  
Claudio Corianò ◽  
Matteo Maria Maglio ◽  
Dimosthenis Theofilopoulos
Keyword(s):  
Momentum Space ◽  
Form Factors ◽  
Conformal Anomaly ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Independent Form ◽  
Stress Energy ◽  
Complete Determination ◽  
Non Local

AbstractWe elaborate on the structure of the conformal anomaly effective action up to 4-th order, in an expansion in the gravitational fluctuations (h) of the background metric, in the flat spacetime limit. For this purpose we discuss the renormalization of 4-point functions containing insertions of stress-energy tensors (4T), in conformal field theories in four spacetime dimensions with the goal of identifying the structure of the anomaly action. We focus on a separation of the correlator into its transverse/traceless and longitudinal components, applied to the trace and conservation Ward identities (WI) in momentum space. These are sufficient to identify, from their hierarchical structure, the anomaly contribution, without the need to proceed with a complete determination of all of its independent form factors. Renormalization induces sequential bilinear graviton-scalar mixings on single, double and multiple trace terms, corresponding to $$R\square ^{-1}$$ R □ - 1 interactions of the scalar curvature, with intermediate virtual massless exchanges. These dilaton-like terms couple to the conformal anomaly, as for the chiral anomalous WIs. We show that at 4T level a new traceless component appears after renormalization. We comment on future extensions of this result to more general backgrounds, with possible applications to non local cosmologies.

INTEGRABLE LATTICE MODELS, GRAPHS AND MODULAR INVARIANT CONFORMAL FIELD THEORIES

1992 ◽  
Vol 07 (03) ◽  
pp. 407-500 ◽  
Author(s):  
P. DI FRANCESCO
Keyword(s):  
Lattice Models ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Compact Lie Groups ◽  
Modular Invariant ◽  
Conformally Invariant ◽  
Conformal Field ◽  
Integrable Lattice ◽  
Modular Invariants ◽  
Integrable Lattice Models

We review the construction of integrable height models attached to graphs, in connection with compact Lie groups. The continuum limit of these models yields conformally invariant field theories. A direct relation between graphs and (Kac–Moody or coset) modular invariants is proposed.

scholarly journals GENERALIZED ABELIAN CHERN-SIMONS THEORIES AND THEIR CONNECTION TO CONFORMAL FIELD THEORIES

1992 ◽  
Vol 07 (19) ◽  
pp. 4477-4486 ◽  
Author(s):  
MARCO A.C. KNEIPP
Keyword(s):  
Three Dimensional ◽  
Magnetic Monopoles ◽  
Field Theories ◽  
Vertex Operators ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Integral Lattice ◽  
Conformal Field ◽  
Free Scalar ◽  
Chern Simons

We discuss the generalization of Abelian Chern-Simons theories when θ-angles and magnetic monopoles are included. We map these three dimensional theories into sectors of two-dimensional conformal field theories. The introduction of θ-angles allows us to establish in a consistent fashion a connection between Abelian Chern-Simons and 2-d free scalar field compactified on a noneven integral lattice. The Abelian Chern-Simons with magnetic monopoles is related to a conformal field theory in which the sum of the charges of the chiral vertex operators inside a correlator is different from zero.

scholarly journals Effective field theory for closed strings near the Hagedorn temperature

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Ram Brustein ◽  
Yoav Zigdon
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Effective Action ◽  
Equations Of Motion ◽  
Flat Space ◽  
Conformal Structure ◽  
Effective Field ◽  
Conformally Invariant ◽  
Conformal Field ◽  
Quartic Interaction

Abstract We discuss interacting, closed, bosonic and superstrings in thermal equilibrium at temperatures close to the Hagedorn temperature in flat space. We calculate S-matrix elements of the strings at the Hagedorn temperature and use them to construct a low-energy effective action for interacting strings near the Hagedorn temperature. We show, in particular, that the four-point amplitude of massless winding modes leads to a positive quartic interaction. Furthermore, the effective field theory has a generalized conformal structure, namely, it is conformally invariant when the temperature is assigned an appropriate scaling dimension. Then, we show that the equations of motion resulting from the effective action possess a winding-mode-condensate background solution above the Hagedorn temperature and present a worldsheet conformal field theory, similar to a Sine-Gordon theory, that corresponds to this solution. We find that the Hagedorn phase transition in our setup is second order, in contrast to a first-order transition that was found previously in different setups.

scholarly journals QUANTUM ENERGY INEQUALITIES IN TWO-DIMENSIONAL CONFORMAL FIELD THEORY

2005 ◽  
Vol 17 (05) ◽  
pp. 577-612 ◽  
Author(s):  
CHRISTOPHER J. FEWSTER ◽  
STEFAN HOLLANDS
Keyword(s):  
Field Theories ◽  
Positive Energy ◽  
Energy Tensor ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Stress Energy Tensor ◽  
Quantum Energy ◽  
Conformal Field ◽  
Quantum Energy Inequalities ◽  
Stress Energy

Quantum energy inequalities (QEIs) are state-independent lower bounds on weighted averages of the stress-energy tensor, and have been established for several free quantum field models. We present rigorous QEI bounds for a class of interacting quantum fields, namely the unitary, positive energy conformal field theories (with stress-energy tensor) on two-dimensional Minkowski space. The QEI bound depends on the weight used to average the stress-energy tensor and the central charge(s) of the theory, but not on the quantum state. We give bounds for various situations: averaging along timelike, null and spacelike curves, as well as over a space-time volume. In addition, we consider boundary conformal field theories and more general "moving mirror" models. Our results hold for all theories obeying a minimal set of axioms which — as we show — are satisfied by all models built from unitary highest-weight representations of the Virasoro algebra. In particular, this includes all (unitary, positive energy) minimal models and rational conformal field theories. Our discussion of this issue collects together (and, in places, corrects) various results from the literature which do not appear to have been assembled in this form elsewhere.

EXACT DYNAMIC THEORIES ON A GIVEN BACKGROUND IN GRAVITATION

1988 ◽  
Vol 03 (11) ◽  
pp. 2651-2679 ◽  
Author(s):  
A.D. POPOVA ◽  
A.N. PETROV
Keyword(s):  
Field Theory ◽  
Gauge Invariance ◽  
Dynamic Stress ◽  
Equations Of Motion ◽  
Dynamic Equations ◽  
Einstein Theory ◽  
Gauge Transformations ◽  
Flat Background ◽  
Stress Energy ◽  
Finite Displacements

In any field theory the variables can always be decomposed into a sum of background and dynamic parts. We analyse exact dynamic theories in which the dynamic field is not small; an arbitrary theory of gravity is meant. In the initial theory the choice of variables is inessential. Dynamic theories constructed for different choices of initial variables which are then decomposed, turn out to be in a certain sense inequivalent. We show that the dynamic stress-energy tensors differ in terms that do not vanish on the solutions both background and dynamic equations of motion. This property is exact, i.e., it is valid irrespective of any approximations. We consider gauge invariance of dynamic theories under gauge transformations induced by finite displacements of the 4-space. We discuss peculiarities of dynamic theories in the Einstein theory with material fields as sources. In the case of flat background the differences in the stress-energy tensors reduce to a divergence of a superpotential.

BRST EXACTNESS OF STRESS-ENERGY TENSORS

1994 ◽  
Vol 09 (12) ◽  
pp. 2033-2065 ◽  
Author(s):  
HIDEO MIYATA ◽  
HIROSHI SUGIMOTO
Keyword(s):  
Lie Algebras ◽  
Simple Root ◽  
Dynkin Diagram ◽  
Field Theories ◽  
General Level ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Stress Energy ◽  
Multiple Integrals ◽  
Extended Dynkin Diagram

BRST commutators in the topological conformal field theories obtained by twisting N=2 theories are evaluated explicitly. By our systematic calculations of the multiple integrals which contain screening operators, the BRST exactness of the twisted stress-energy tensors is deduced for classical simple Lie algebras and general level k. We can see that the paths of integrations do not affect the result, and further, the N=2 coset theories are obtained by deleting two simple roots with Kac-label 1 from the extended Dynkin diagram; in other words, by not performing the integrations over the variables corresponding to the two simple roots of Kac-Moody algebras. It is also shown that a series of N=1 theories are generated in the same way by deleting one simple root with Kac-label 2.

scholarly journals SYMMETRIC SUBGROUPS OF GAUGED SUPERGRAVITIES AND AdS STRING THEORY VERTEX OPERATORS

1999 ◽  
Vol 14 (07) ◽  
pp. 517-525 ◽  
Author(s):  
L. DOLAN ◽  
M. LANGHAM
Keyword(s):  
Gauge Symmetry ◽  
String Theory ◽  
Massless Particle ◽  
Field Theories ◽  
Vertex Operators ◽  
Conformal Field Theories ◽  
Particle Content ◽  
Conformal Field ◽  
Monster Group ◽  
Symmetric Subgroups

We show how the gauge symmetry representations of the massless particle content of gauged supergravities that arise in the AdS/CFT correspondences can be derived from symmetric subgroups to be carried by string theory vertex operators, although explicit vertex operator constructions of the IIB string on AdS remain elusive. Our symmetry mechanism parallels the construction of representations of the Monster group and affine algebras in terms of twisted conformal field theories, and may serve as a guide to a perturbative description of the IIB string on AdS.

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