scholarly journals NEW DISCRETE STATES IN TWO-DIMENSIONAL SUPERGRAVITY

2007 ◽  
Vol 22 (07) ◽  
pp. 1375-1394 ◽  
Author(s):  
DIMITRI POLYAKOV
Keyword(s):  
Operator Algebra ◽  
Higher Dimensions ◽  
Two Dimensions ◽  
Field Theories ◽  
Two Dimensional ◽  
Discrete States ◽  
Structure Constants ◽  
Area Preserving ◽  
Volume Preserving ◽  
Lowering Operator

Two-dimensional string theory is known to contain the set of discrete states that are the SU (2) multiplets generated by the lowering operator of the SU (2) current algebra. Their structure constants are defined by the area preserving diffeomorphisms in two dimensions. In this paper we show that the interaction of d = 2 superstrings with the superconformal β - γ ghosts enlarges the actual algebra of the dimension 1 currents and hence the new ghost-dependent discrete states appear. Generally, these states are the SU (N) multiplets if the algebra includes the currents of ghost numbers n : -N ≤ n ≤ N - 2, not related by picture changing. We compute the structure constants of these ghost-dependent discrete states for N = 3 and express them in terms of SU (3) Clebsch–Gordan coefficients, relating this operator algebra to the volume preserving diffeomorphisms in d = 3. For general N, the operator algebra is conjectured to be isomorphic to SDiff (N). This points at possible holographic relations between two-dimensional superstrings and field theories in higher dimensions.

scholarly journals INTERACTION OF DISCRETE STATES IN TWO-DIMENSIONAL STRING THEORY

1991 ◽  
Vol 06 (35) ◽  
pp. 3273-3281 ◽  
Author(s):  
I. R. KLEBANOV ◽  
A. M. POLYAKOV
Keyword(s):  
String Theory ◽  
Effective Action ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Infinite Dimensional ◽  
Dimensional Group ◽  
Discrete States ◽  
Structure Constants ◽  
Area Preserving

We study the couplings of discrete states that appear in the string theory embedded in two dimensions, and show that they are given by the structure constants of the group of area preserving diffeomorphisms. We propose an effective action for these states, which is itself invariant under this infinite-dimensional group.

scholarly journals INTERACTIONS OF DISCRETE STATES WITH NONZERO GHOST NUMBER IN c = 1 2D GRAVITY

1992 ◽  
Vol 07 (29) ◽  
pp. 2723-2730 ◽  
Author(s):  
NOBUYOSHI OHTA ◽  
HISAO SUZUKI
Keyword(s):  
Quantum Gravity ◽  
Vertex Operator ◽  
Effective Action ◽  
2D Gravity ◽  
Ghost Number ◽  
Two Dimensional ◽  
Discrete States ◽  
Structure Constants ◽  
Area Preserving ◽  
Operator Representations

We study the interactions of the discrete states with nonzero ghost number in c = 1 two-dimensional (2D) quantum gravity. By using the vertex operator representations, it is shown that their interactions are given by the structure constants of the group of the area preserving diffeomorphism similar to those of vanishing ghost number. The effective action for these states is also worked out. The result suggests that the whole system has a BRST-like symmetry.

scholarly journals On 2d CFTs that interpolate between minimal models

2019 ◽  
Vol 6 (6) ◽  
Author(s):  
Sylvain Ribault
Keyword(s):  
Correlation Functions ◽  
Central Charge ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Conformal Blocks ◽  
Conformal Field ◽  
Exactly Solvable ◽  
Structure Constants

We investigate exactly solvable two-dimensional conformal field theories that exist at generic values of the central charge, and that interpolate between A-series or D-series minimal models. When the central charge becomes rational, correlation functions of these CFTs may tend to correlation functions of minimal models, or diverge, or have finite limits which can be logarithmic. These results are based on analytic relations between four-point structure constants and residues of conformal blocks.

scholarly journals ON TWO-DIMENSIONAL QUASITOPOLOGICAL FIELD THEORIES

2009 ◽  
Vol 24 (32) ◽  
pp. 6105-6121 ◽  
Author(s):  
P. TEOTONIO-SOBRINHO ◽  
C. MOLINA ◽  
N. YOKOMIZO
Keyword(s):  
Hopf Algebras ◽  
Gauge Theories ◽  
Local Symmetry ◽  
Two Dimensions ◽  
Field Theories ◽  
Partition Functions ◽  
Wilson Loops ◽  
Two Dimensional ◽  
Lattice Field ◽  
Expected Values

We study a class of lattice field theories in two dimensions that includes gauge theories. We show that in these theories it is possible to implement a broader notion of local symmetry, based on semisimple Hopf algebras. A character expansion is developed for the quasitopological field theories, and partition functions are calculated with this tool. Expected values of generalized Wilson loops are defined and studied with the character expansion.

scholarly journals A toy model of discretized gravity in two dimensions and its extensions

2017 ◽  
Vol 32 (28) ◽  
pp. 1750149
Author(s):  
Marcello Rotondo ◽  
Shin’ichi Nojiri
Keyword(s):  
Quantum Gravity ◽  
Continuum Limit ◽  
Higher Dimensions ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Expectation Value ◽  
Dynamical Triangulation ◽  
Physical Quantities ◽  
Euclidean Signature

We propose a toy model of quantum gravity in two dimensions with Euclidean signature. The model is given by a kind of discretization which is different from the dynamical triangulation. We show that there exists a continuum limit and we can calculate some physical quantities such as the expectation value of the area, that is, the volume of the two-dimensional Euclidean spacetime. We also consider the extensions of the model to higher dimensions.

scholarly journals QUASITOPOLOGICAL FIELD THEORIES IN TWO DIMENSIONS AS SOLUBLE MODELS

1998 ◽  
Vol 13 (21) ◽  
pp. 3667-3689 ◽  
Author(s):  
BRUNO G. CARNEIRO DA CUNHA ◽  
PAULO TEOTONIO-SOBRINHO
Keyword(s):  
Orientable Surface ◽  
Two Dimensions ◽  
Field Theories ◽  
Partition Functions ◽  
Two Dimensional ◽  
Yang Mills ◽  
Lattice Field ◽  
Topological Field ◽  
Universality Classes ◽  
Area Limit

We study a class of lattice field theories in two dimensions that includes Yang–Mills and generalized Yang–Mills theories as particular examples. Given a two-dimensional orientable surface of genus g, the partition function Z is defined for a triangulation consisting of n triangles of size ∊. The reason these models are called quasitopological is that Z depends on g, n and ∊ but not on the details of the triangulation. They are also soluble in the sense that the computation of their partition functions for a two-dimensional lattice can be reduced to a soluble one-dimensional problem. We show that the continuum limit is well defined if the model approaches a topological field theory in the zero area limit, i.e. ∊→0 with finite n. We also show that the universality classes of such quasitopological lattice field theories can be easily classified.

scholarly journals Exclusion inside or at the border of conformal bootstrap continent

2020 ◽  
Vol 35 (06) ◽  
pp. 2050036
Author(s):  
Yu Nakayama
Keyword(s):  
Bound States ◽  
Pauli Exclusion Principle ◽  
Higher Dimensions ◽  
Two Dimensions ◽  
Field Theories ◽  
Exclusion Principle ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Conformal Bootstrap ◽  
Anomalous Dimensions

How large can anomalous dimensions be in conformal field theories? What can we do to attain larger values? One attempt to obtain large anomalous dimensions efficiently is to use the Pauli exclusion principle. Certain operators constructed out of constituent fermions cannot form bound states without introducing nontrivial excitations. To assess the efficiency of this mechanism, we compare them with the numerical conformal bootstrap bound as well as with other interacting field theory examples. In two dimensions, it turns out to be the most efficient: it saturates the bound and is located at the (second) kink. In higher dimensions, it more or less saturates the bound but it may be slightly inside.

OPERATOR ALGEBRA IN TWO-DIMENSIONAL CONFORMAL FIELD THEORY CONTAINING SPIN 4/3 “PARAFERMIONIC” CONSERVED CURRENTS

1991 ◽  
Vol 06 (11) ◽  
pp. 2005-2023 ◽  
Author(s):  
R.H. POGHOSSIAN
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Operator Algebra ◽  
Closed Operator ◽  
Operator Product ◽  
Two Dimensional ◽  
Conformal Field ◽  
Structure Constants ◽  
Conserved Currents

Recently Zamolodchikov and Fateev have constructed a series of models of the two-dimensional conformal field theory containing spin 4/3 nonlocal (parafermion) currents. From degenerated fields one can construct a closed operator algebra with respect to the operator product expansions. All the structure constants of this algebra are computed in this paper.

A few solvable two-dimensional quantum field theories (QFT)

2021 ◽  
pp. 721-746
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Quantum Electrodynamics ◽  
Particle Physics ◽  
Chiral Symmetry Breaking ◽  
Spin Model ◽  
Two Dimensions ◽  
Thirring Model ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Two Dimensional

The chapter is devoted to several two-dimensional quantum field theories (QFT), whose properties can be determined by non-perturbative methods. The Schwinger model, a model of two-dimensional quantum electrodynamics (QED) with massless fermions, illustrates the properties of confinement, spontaneous chiral symmetry breaking, asymptotic freedom and anomalies, properties one also expects in particle physics from quantum chromodynamics. The equivalence between the massive Thirring model, a fermion model with current–current interaction, and the sine-Gordon model is derived, using the bozonisation technique. The bosonization technique, based on an identity for Cauchy determinants, establishes relations, specific to two dimensions, between fermion and boson local field theories. Several generalized Thirring model are also discussed. In the discussion of the O(N) non-linear σ-model, it has been noticed that the Abelian case N = 2 is special, because the renormalization group (RG) β-function vanishes in two dimensions. The corresponding O(2) invariant spin model is especially interesting: it provides an example of the celebrated Kosterlitz–Thouless (KT) phase transition and will be studied elsewhere. This chapter also provides the necessary technical background for such an investigation.

scholarly journals THE ULTRAVIOLET PROPERTIES OF SUPERSYMMETRIC FIELD THEORIES

1989 ◽  
Vol 04 (08) ◽  
pp. 1871-1912 ◽  
Author(s):  
P. S. HOWE ◽  
K. S. STELLE
Keyword(s):  
Perturbation Theory ◽  
Higher Dimensions ◽  
Background Field ◽  
Field Method ◽  
Field Theories ◽  
Ultraviolet Divergence ◽  
Two Dimensional ◽  
Yang Mills ◽  
Supersymmetric Field Theories ◽  
Background Field Method

We review the structure of ultraviolet divergence cancellations in supersymmetric field theories. We discuss the various nonrenormalization theorems of superspace perturbation theory, both for extended and for simple supersymmetry. These theorems and the background field method are applied to super Yang-Mills theories in four and higher dimensions, to supergravity theories and to two-dimensional supersymmetric nonlinear σ-models.

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