scholarly journals THE BROKEN PHASE OF THE TOPOLOGICAL σ MODEL

1995 ◽  
Vol 10 (11) ◽  
pp. 1553-1575 ◽  
Author(s):  
A.V. YUNG
Keyword(s):  
Moduli Space ◽  
Correlation Functions ◽  
Vacuum Energy ◽  
Brst Symmetry ◽  
Vacuum State ◽  
Target Space ◽  
Topological Phase ◽  
Coordinate Dependence ◽  
Vacuum States ◽  
Hole Geometry

The topological σ model with the semi-infinite cigar-like target space (black hole geometry) is considered. It is shown to possess unsuppressed instantons. The noncompactness of the moduli space of these instantons is responsible for an unusual physics. There is a stable vacuum state in which the vacuum energy is 0, and correlation functions are numbers; thus the model is in the topological phase. However, there are other vacuum states in which correlation functions show the coordinate dependence. Estimation of the vacuum energy indicates that it is nonzero. The states are interpreted as the ones with broken BRST symmetry.

scholarly journals INSTANTON DYNAMICS IN THE BROKEN PHASE OF THE TOPOLOGICAL SIGMA MODEL

1996 ◽  
Vol 11 (05) ◽  
pp. 951-974 ◽  
Author(s):  
A.V. YUNG
Keyword(s):  
Black Hole ◽  
Correlation Functions ◽  
Arbitrary Number ◽  
Sigma Model ◽  
Vacuum Energy ◽  
Brst Symmetry ◽  
Coulomb Gas ◽  
Target Space ◽  
Coordinate Dependence

The topological σ model with the black hole metric of the target space is considered. It has been shown before that this model is in the phase with BRST symmetry broken. In particular, the vacuum energy is nonzero and correlation functions of observables show the coordinate dependence. However, these quantities turn out to be infrared-divergent. It is shown here that IR divergences disappear after the sum over an arbitrary number of additional instanton–anti-instanton pairs is performed. The model appears to be equivalent to the Coulomb gas/sine–Gordon system.

scholarly journals String theory on AdS3 × M7 in the tensionless limit

2020 ◽  
Vol 29 (06) ◽  
pp. 2030005
Author(s):  
Gaston Giribet
Keyword(s):  
String Theory ◽  
Moduli Space ◽  
Correlation Functions ◽  
Target Space ◽  
Special Point ◽  
String Length ◽  
Special Limit

We review old and recent results on a special limit of string theory on [Formula: see text] with pure NS–NS fluxes: the limit in which the string length [Formula: see text] equals the [Formula: see text] radius [Formula: see text]. At this point of the moduli space, the theory exhibits special properties, which we discuss. Special attention is focused on features of correlation functions that are related to the noncompactness of the boundary CFT target space, and on how these features change when the point [Formula: see text] is approached. Also, we briefly review the recent proposals for exact realizations of AdS/CFT correspondence at this special point.

scholarly journals The Volume of the Quiver Vortex Moduli Space

2021 ◽  
Author(s):  
Kazutoshi Ohta ◽  
Norisuke Sakai
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Riemann Surfaces ◽  
Gauge Theories ◽  
Target Space ◽  
Contour Integral ◽  
Quiver Gauge Theory ◽  
Volume Formula ◽  
Volume Operator ◽  
Space Volume

Abstract We study the moduli space volume of BPS vortices in quiver gauge theories on compact Riemann surfaces. The existence of BPS vortices imposes constraints on the quiver gauge theories. We show that the moduli space volume is given by a vev of a suitable cohomological operator (volume operator) in a supersymmetric quiver gauge theory, where BPS equations of the vortices are embedded. In the supersymmetric gauge theory, the moduli space volume is exactly evaluated as a contour integral by using the localization. Graph theory is useful to construct the supersymmetric quiver gauge theory and to derive the volume formula. The contour integral formula of the volume (generalization of the Jeffrey-Kirwan residue formula) leads to the Bradlow bounds (upper bounds on the vorticity by the area of the Riemann surface divided by the intrinsic size of the vortex). We give some examples of various quiver gauge theories and discuss properties of the moduli space volume in these theories. Our formula are applied to the volume of the vortex moduli space in the gauged non-linear sigma model with CPN target space, which is obtained by a strong coupling limit of a parent quiver gauge theory. We also discuss a non-Abelian generalization of the quiver gauge theory and “Abelianization” of the volume formula.

scholarly journals YUKAWA COUPLINGS FOR BOSONIC ZN ORBIFOLDS: THEIR MODULI AND TWISTED SECTOR DEPENDENCE

1992 ◽  
Vol 07 (33) ◽  
pp. 3059-3070 ◽  
Author(s):  
S. STIEBERGER ◽  
D. JUNGNICKEL ◽  
J. LAUER ◽  
M. SPALIŃSKI
Keyword(s):  
Correlation Functions ◽  
Target Space ◽  
Twisted Sector ◽  
Yukawa Couplings ◽  
Point Correlation ◽  
Field Correlation ◽  
Twist Fields

The three-point correlation functions with twist fields are determined for bosonic ZN orbifolds. Both the choice of the modular background (compatible with the twist) and of the (higher) twisted sectors involved are fully general. We point out a necessary restriction on the set of instantons contributing to twist field correlation functions not obtained in previous calculations. Our results show that the theory is target space duality invariant.

scholarly journals Harmonic analysis of 2d CFT partition functions

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Nathan Benjamin ◽  
Scott Collier ◽  
A. Liam Fitzpatrick ◽  
Alexander Maloney ◽  
Eric Perlmutter
Keyword(s):  
Partition Function ◽  
Harmonic Analysis ◽  
Moduli Space ◽  
Target Space ◽  
Field Theories ◽  
Partition Functions ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Operator Spectrum

Abstract We apply the theory of harmonic analysis on the fundamental domain of SL(2, ℤ) to partition functions of two-dimensional conformal field theories. We decompose the partition function of c free bosons on a Narain lattice into eigenfunctions of the Laplacian of worldsheet moduli space ℍ/SL(2, ℤ), and of target space moduli space O(c, c; ℤ)\O(c, c; ℝ)/O(c)×O(c). This decomposition manifests certain properties of Narain theories and ensemble averages thereof. We extend the application of spectral theory to partition functions of general two-dimensional conformal field theories, and explore its meaning in connection to AdS3 gravity. An implication of harmonic analysis is that the local operator spectrum is fully determined by a certain subset of degeneracies.

scholarly journals Correlations and commuting transfer matrices in integrable unitary circuits

2022 ◽  
Vol 12 (1) ◽  
Author(s):  
Pieter W. Claeys ◽  
Jonah Herzog-Arbeitman ◽  
Austen Lamacraft
Keyword(s):  
Correlation Functions ◽  
Exceptional Point ◽  
Baxter Equation ◽  
Matrix Formalism ◽  
Transfer Matrices ◽  
Local Conservation ◽  
Vacuum States ◽  
Integrable Spin ◽  
Commuting Transfer Matrices ◽  
Bethe Equations

We consider a unitary circuit where the underlying gates are chosen to be \check{R}Ř-matrices satisfying the Yang-Baxter equation and correlation functions can be expressed through a transfer matrix formalism. These transfer matrices are no longer Hermitian and differ from the ones guaranteeing local conservation laws, but remain mutually commuting at different values of the spectral parameter defining the circuit. Exact eigenstates can still be constructed as a Bethe ansatz, but while these transfer matrices are diagonalizable in the inhomogeneous case, the homogeneous limit corresponds to an exceptional point where multiple eigenstates coalesce and Jordan blocks appear. Remarkably, the complete set of (generalized) eigenstates is only obtained when taking into account a combinatorial number of nontrivial vacuum states. In all cases, the Bethe equations reduce to those of the integrable spin-1 chain and exhibit a global SU(2) symmetry, significantly reducing the total number of eigenstates required in the calculation of correlation functions. A similar construction is shown to hold for the calculation of out-of-time-order correlations.

scholarly journals Higgs Branch, Hyper-Kähler Quotient and Duality in SUSY N = 2 Yang–Mills Theories

1997 ◽  
Vol 12 (27) ◽  
pp. 4907-4931 ◽  
Author(s):  
I. Antoniadis ◽  
B. Pioline
Keyword(s):  
Moduli Space ◽  
Gauge Theories ◽  
Geometric Interpretation ◽  
Low Energy ◽  
Target Space ◽  
Field Theories ◽  
Yang Mills ◽  
Coulomb Phase ◽  
Supersymmetric Field Theories ◽  
Energy Theory

Low-energy limits of N = 2 supersymmetric field theories in the Higgs branch are described in terms of a nonlinear four-dimensional σ-model on a hyper-Kähler target space, classically obtained as a hyper-Kähler quotient of the original flat hypermultiplet space by the gauge group. We review in a pedagogical way this construction, and illustrate it in various examples, with special attention given to the singularities emerging in the low-energy theory. In particular, we thoroughly study the Higgs branch singularity of Seiberg–Witten SU(2) theory with Nf flavors, interpreted by Witten as a small instanton singularity in the moduli space of one instanton on ℝ4. By explicitly evaluating the metric, we show that this Higgs branch coincides with the Higgs branch of a U(1) N = 2 SUSY theory with the number of flavors predicted by the singularity structure of Seiberg–Witten's theory in the Coulomb phase. We find another example of Higgs phase duality, namely between the Higgs phases of U(Nc)Nf flavors and U(Nf-Nc)Nf flavors theories, by using a geometric interpretation due to Biquard et al. This duality may be relevant for understanding Seiberg's conjectured duality Nc ↔ Nf-Nc in N = 1 SUSY SU(Nc) gauge theories.

scholarly journals Evaluation of the Cosmological Constant in Inflation with a Massive Nonminimal Scalar Field

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Jung-Jeng Huang
Keyword(s):  
Scalar Field ◽  
Dispersion Relation ◽  
Energy Density ◽  
Cosmological Constant ◽  
Vacuum Energy ◽  
Vacuum State ◽  
Energy Scale ◽  
Quantum Evolution ◽  
Vacuum Energy Density ◽  
De Sitter

In Schrödinger picture we study the possible effects of trans-Planckian physics on the quantum evolution of massive nonminimally coupled scalar field in de Sitter space. For the nonlinear Corley-Jacobson type dispersion relations with quartic or sextic correction, we obtain the time evolution of the vacuum state wave functional during slow-roll inflation and calculate explicitly the corresponding expectation value of vacuum energy density. We find that the vacuum energy density is finite. For the usual dispersion parameter choice, the vacuum energy density for quartic correction to the dispersion relation is larger than for sextic correction, while for some other parameter choices, the vacuum energy density for quartic correction is smaller than for sextic correction. We also use the backreaction to constrain the magnitude of parameters in nonlinear dispersion relation and show how the cosmological constant depends on the parameters and the energy scale during the inflation at the grand unification phase transition.

scholarly journals USE OF NILPOTENT WEIGHTS IN LOGARITHMIC CONFORMAL FIELD THEORIES

2003 ◽  
Vol 18 (25) ◽  
pp. 4747-4770 ◽  
Author(s):  
S. MOGHIMI-ARAGHI ◽  
S. ROUHANI ◽  
M. SAADAT
Keyword(s):  
Correlation Functions ◽  
Brst Symmetry ◽  
Momentum Tensor ◽  
Field Theories ◽  
Scale Transformation ◽  
Operator Product ◽  
Conformal Weight ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Point Correlation

We show that logarithmic conformal field theories may be derived using nilpotent scale transformation. Using such nilpotent weights we derive properties of LCFT's, such as two and three point correlation functions solely from symmetry arguments. Singular vectors and the Kac determinant may also be obtained using these nilpotent variables, hence the structure of the four point functions can also be derived. This leads to non homogeneous hypergeometric functions. Also we consider LCFT's near a boundary. Constructing "superfields" using a nilpotent variable, we show that the superfield of conformal weight zero, composed of the identity and the pseudo identity is related to a superfield of conformal dimension two, which comprises of energy momentum tensor and its logarithmic partner. This device also allows us to derive the operator product expansion for logarithmic operators. Finally we discuss the AdS/LCFT correspondence and derive some correlation functions and a BRST symmetry.

Superposition and entanglement of two-mode squeezed vacuum states

2018 ◽  
Vol 16 (01) ◽  
pp. 1850003 ◽  
Author(s):  
Amir Karimi
Keyword(s):  
Radiation Field ◽  
Vacuum State ◽  
Squeezed Vacuum ◽  
Vacuum States ◽  
Squeezing Operator ◽  
Parity Operator

In this paper, by using the parity operator as well as the two-mode squeezing operator, we define new operators which by the action of them on the vacuum state of the two-mode radiation field, superposition of two two-mode squeezed vacuum states and entangled two-mode squeezed vacuum states are generated.

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