scholarly journals UNITARITY RELATIONS IN c=1 LIOUVILLE THEORY

1992 ◽  
Vol 07 (28) ◽  
pp. 2647-2657 ◽  
Author(s):  
DAVID A. LOWE
Keyword(s):  
Field Theory ◽  
Cosmological Constant ◽  
Particle Creation ◽  
Liouville Theory ◽  
Tree Level ◽  
S Matrix ◽  
The Matrix ◽  
Higher Genus ◽  
Genus One ◽  
Branch Cuts

We consider the S-matrix of c=1 Liouville theory with vanishing cosmological constant. We examine some of the constraints imposed by unitarity. These completely determine (N,2) amplitudes at tree level in terms of the (N,1) amplitudes when the "plus" tachyon momenta take generic values. A surprising feature of the matrix model results is the lack of particle creation branch cuts in the higher genus amplitudes. In fact, we show that the naive field theory limit of Liouville theory would predict such branch cuts. However, unitarity in the full string theory ensures that such cuts do not appear in genus one (N,1) amplitudes. We conclude with some comments about the genus one (N,2) amplitudes.

scholarly journals On the quantum field theory of the gravitational interactions

2018 ◽  
Author(s):  
Damiano Anselmi
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Cosmological Constant ◽  
Gauge Coupling ◽  
Cosmological Term ◽  
Power Counting ◽  
Quantum Field ◽  
Higher Derivative ◽  
S Matrix ◽  
Local Quantum

We study the main options for a unitary and renormalizable, local quantum field theory of the gravitational interactions. The first model is a Lee-Wick superrenormalizable higher-derivative gravity, formulated as a nonanalytically Wick rotated Euclidean theory. We show that, under certain conditions, the $S$ matrix is unitary when the cosmological constant vanishes. The model is the simplest of its class. However, infinitely many similar options are allowed, which raises the issue of uniqueness. To deal with this problem, we propose a new quantization prescription, by doubling the unphysical poles of the higher-derivative propagators and turning them into Lee-Wick poles. The Lagrangian of the simplest theory of quantum gravity based on this idea is the linear combination of $R$, $R_{\mu \nu}R^{\mu \nu }$, $R^{2}$ and the cosmological term. Only the graviton propagates in the cutting equations and, when the cosmological constant vanishes, the $S$ matrix is unitary. The theory satisfies the locality of counterterms and is renormalizable by power counting. It is unique in the sense that it is the only one with a dimensionless gauge coupling.

scholarly journals Tree-level S-matrix of superstring field theory with homotopy algebra structure

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Hiroshi Kunitomo
Keyword(s):  
Field Theory ◽  
String Field Theory ◽  
Heterotic String ◽  
Field Theories ◽  
Tree Level ◽  
Algebra Structure ◽  
Type Ii ◽  
S Matrix ◽  
Homotopy Algebra

Abstract We show that the tree-level S-matrices of the superstring field theories based on the homotopy-algebra structure agree with those obtained in the first-quantized formulation. The proof is given in detail for the heterotic string field theory. The extensions to the type II and open superstring field theories are straightforward.

VIRASORO CONSTRAINTS ON THE MATRIX-MODEL PARTITION FUNCTION AND STRING FIELD THEORY

1992 ◽  
Vol 07 (07) ◽  
pp. 1553-1581 ◽  
Author(s):  
ASHOKE SEN
Keyword(s):  
Field Theory ◽  
Partition Function ◽  
Matrix Model ◽  
String Field Theory ◽  
Minimal Model ◽  
Differential Operators ◽  
Tree Level ◽  
Virasoro Constraints ◽  
The Matrix ◽  
The One

The one-matrix model at the kth multicritical point is known to describe the (2, 2k–1) minimal model coupled to gravity, and the partition function of this model is known to obey a set of Virasoro constraints generated by a set of differential operators Ln. Working at the tree level of string theory, and using the Feigin-Fuchs description of the (2, 2k–1) minimal model, we show that the Virasoro constraints generated by Li (0≤i≤k−2) can be identified with a set of gauge symmetries of the corresponding string field theory.

scholarly journals Local BCJ numerators for ten-dimensional SYM at one loop

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Elliot Bridges ◽  
Carlos R. Mafra
Keyword(s):  
Field Theory ◽  
Previous Analysis ◽  
Tree Level ◽  
Yang Mills ◽  
Analogous Manner ◽  
Different Color ◽  
Genus One ◽  
Super Yang Mills Theory

Abstract We obtain local numerators satisfying the BCJ color-kinematics duality at one loop for super-Yang-Mills theory in ten dimensions. This is done explicitly for six points via the field-theory limit of the genus-one open superstring correlators for different color orderings, in an analogous manner to an earlier derivation of local BCJ-satisfying numerators at tree level from disk correlators. These results solve an outstanding puzzle from a previous analysis where the six-point numerators did not satisfy the color-kinematics duality.

scholarly journals LIOUVILLE FIELD THEORY: A DECADE AFTER THE REVOLUTION

2004 ◽  
Vol 19 (17n18) ◽  
pp. 2771-2930 ◽  
Author(s):  
YU NAKAYAMA
Keyword(s):  
Field Theory ◽  
Liouville Theory ◽  
Original Material ◽  
The Matrix ◽  
Boundary States ◽  
Recent Developments ◽  
Dual Action ◽  
Structure Constants ◽  
Bulk Structure ◽  
Liouville Field Theory

We review recent developments (up to January 2004) of the Liouville field theory and its matrix model dual. This review consists of two parts. In part I, we review the bosonic Liouville theory. After briefly reviewing the necessary background, we discuss the bulk structure constants (the DOZZ formula) and the boundary states (the FZZT brane and the ZZ brane). Various applications are also presented. In part II, we review the supersymmetric extension of the Liouville theory. We first discuss the bulk structure constants and the branes as in the bosonic Liouville theory, and then we present the matrix dual descriptions with some applications. This review also includes some original material such as the derivation of the conjectured dual action for the [Formula: see text] Liouville theory from other known dualities.

scholarly journals Towards Feynman rules for conformal blocks

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sarah Hoback ◽  
Sarthak Parikh
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Hypergeometric Functions ◽  
Power Series Expansion ◽  
Effective Field ◽  
Conformal Block ◽  
Tree Level ◽  
Conformal Blocks ◽  
Simple Set ◽  
Feynman Rules

Abstract We conjecture a simple set of “Feynman rules” for constructing n-point global conformal blocks in any channel in d spacetime dimensions, for external and exchanged scalar operators for arbitrary n and d. The vertex factors are given in terms of Lauricella hypergeometric functions of one, two or three variables, and the Feynman rules furnish an explicit power-series expansion in powers of cross-ratios. These rules are conjectured based on previously known results in the literature, which include four-, five- and six-point examples as well as the n-point comb channel blocks. We prove these rules for all previously known cases, as well as two new ones: the seven-point block in a new topology, and all even-point blocks in the “OPE channel.” The proof relies on holographic methods, notably the Feynman rules for Mellin amplitudes of tree-level AdS diagrams in a scalar effective field theory, and is easily applicable to any particular choice of a conformal block beyond those considered in this paper.

scholarly journals On the Modular Operator of Mutli-component Regions in Chiral CFT

2021 ◽  
Author(s):  
Stefan Hollands
Keyword(s):  
Field Theory ◽  
Integral Equation ◽  
Hilbert Problem ◽  
Matrix Elements ◽  
New Approach ◽  
Conformal Field ◽  
The Matrix ◽  
Kms Condition ◽  
Modular Operator ◽  
Riemann Hilbert Problem

AbstractWe introduce a new approach to find the Tomita–Takesaki modular flow for multi-component regions in general chiral conformal field theory. Our method is based on locality and analyticity of primary fields as well as the so-called Kubo–Martin–Schwinger (KMS) condition. These features can be used to transform the problem to a Riemann–Hilbert problem on a covering of the complex plane cut along the regions, which is equivalent to an integral equation for the matrix elements of the modular Hamiltonian. Examples are considered.

scholarly journals More on holographic correlators: twisted and dimensionally reduced structures

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Connor Behan ◽  
Pietro Ferrero ◽  
Xinan Zhou
Keyword(s):  
Field Theory ◽  
Theoretical Data ◽  
Infinite Family ◽  
Tree Level ◽  
Chiral Algebra ◽  
Perfect Agreement ◽  
Four Dimensions ◽  
Independent Field ◽  
Superconformal Theories ◽  
Emergent Structure

Abstract Recently four-point holographic correlators with arbitrary external BPS operators were constructively derived in [1, 2] at tree-level for maximally superconformal theories. In this paper, we capitalize on these theoretical data, and perform a detailed study of their analytic properties. We point out that these maximally supersymmetric holographic correlators exhibit a hidden dimensional reduction structure à la Parisi and Sourlas. This emergent structure allows the correlators to be compactly expressed in terms of only scalar exchange diagrams in a dimensionally reduced spacetime, where formally both the AdS and the sphere factors have four dimensions less. We also demonstrate the superconformal properties of holographic correlators under the chiral algebra and topological twistings. For AdS5× S5 and AdS7× S4, we obtain closed form expressions for the meromorphic twisted correlators from the maximally R-symmetry violating limit of the holographic correlators. The results are compared with independent field theory computations in 4d $$ \mathcal{N} $$ N = 4 SYM and the 6d (2, 0) theory, finding perfect agreement. For AdS4× S7, we focus on an infinite family of near-extremal four-point correlators, and extract various protected OPE coefficients from supergravity. These OPE coefficients provide new holographic predictions to be matched by future supersymmetric localization calculations. In deriving these results, we also develop many technical tools which should have broader applicability beyond studying holographic correlators.

scholarly journals Soft photon theorem in the small negative cosmological constant limit

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Nabamita Banerjee ◽  
Karan Fernandes ◽  
Arpita Mitra
Keyword(s):  
Cosmological Constant ◽  
Tree Level ◽  
Leading Order ◽  
Asymptotically Flat ◽  
Soft Factor ◽  
Flat Spacetime ◽  
Electromagnetic Interactions ◽  
Flat Spacetimes ◽  
Perturbative Corrections ◽  
Soft Factors

Abstract We study the effect of electromagnetic interactions on the classical soft theorems on an asymptotically AdS background in 4 spacetime dimensions, in the limit of a small cosmological constant or equivalently a large AdS radius l. This identifies 1/l2 perturbative corrections to the known asymptotically flat spacetime leading and subleading soft factors. Our analysis is only valid to leading order in 1/l2. The leading soft factor can be expected to be universal and holds beyond tree level. This allows us to derive a 1/l2 corrected Ward identity, following the known equivalence between large gauge Ward identities and soft theorems in asymptotically flat spacetimes.

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