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 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 ON TOPOLOGICAL SUSCEPTIBILITY, VACUUM ENERGY AND THETA DEPENDENCE IN GLUODYNAMICS

1998 ◽  
Vol 13 (24) ◽  
pp. 1955-1967 ◽  
Author(s):  
IGOR HALPERIN ◽  
ARIEL ZHITNITSKY
Keyword(s):  
Partition Function ◽  
Correlation Functions ◽  
Arbitrary Number ◽  
Density Operator ◽  
Heavy Fermion ◽  
Vacuum Energy ◽  
Gluon Condensate ◽  
Momentum Correlation ◽  
Zero Momentum ◽  
Topological Density

We suggest that the topological susceptibility in gluodynamics can be found in terms of the gluon condensate using renormalizability and heavy fermion representation of the anomaly. Analogous relations can also be obtained for other zero-momentum correlation functions involving the topological density operator. Using these relations, we find the θ dependence of the condensates <GG>, [Formula: see text] and of the partition function for small θ and an arbitrary number of colors.

scholarly journals Long way to Ricci flatness

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Jin Chen ◽  
Chao-Hsiang Sheu ◽  
Mikhail Shifman ◽  
Gianni Tallarita ◽  
Alexei Yung
Keyword(s):  
Sigma Model ◽  
Ultra Violet ◽  
The Other ◽  
Target Space ◽  
Linear Sigma Model ◽  
Close Relative ◽  
Two Dimensional ◽  
World Sheet ◽  
Ricci Flat ◽  
The World

Abstract We study two-dimensional weighted $$ \mathcal{N} $$ N = (2) supersymmetric ℂℙ models with the goal of exploring their infrared (IR) limit. 𝕎ℂℙ(N,$$ \tilde{N} $$ N ˜ ) are simplified versions of world-sheet theories on non-Abelian strings in four-dimensional $$ \mathcal{N} $$ N = 2 QCD. In the gauged linear sigma model (GLSM) formulation, 𝕎ℂℙ(N,$$ \tilde{N} $$ N ˜ ) has N charges +1 and $$ \tilde{N} $$ N ˜ charges −1 fields. As well-known, at $$ \tilde{N} $$ N ˜ = N this GLSM is conformal. Its target space is believed to be a non-compact Calabi-Yau manifold. We mostly focus on the N = 2 case, then the Calabi-Yau space is a conifold. On the other hand, in the non-linear sigma model (NLSM) formulation the model has ultra-violet logarithms and does not look conformal. Moreover, its metric is not Ricci-flat. We address this puzzle by studying the renormalization group (RG) flow of the model. We show that the metric of NLSM becomes Ricci-flat in the IR. Moreover, it tends to the known metric of the resolved conifold. We also study a close relative of the 𝕎ℂℙ model — the so called zn model — which in actuality represents the world sheet theory on a non-Abelian semilocal string and show that this zn model has similar RG properties.

scholarly journals Correlation functions in finite temperature CFT and black hole singularities

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
D. Rodriguez-Gomez ◽  
J.G. Russo
Keyword(s):  
Black Hole ◽  
Event Horizon ◽  
Correlation Functions ◽  
Finite Temperature ◽  
Proper Time ◽  
Black Brane ◽  
Point Function ◽  
Black Hole Singularity ◽  
Point Correlation ◽  
Scaling Dimension

Abstract We compute thermal 2-point correlation functions in the black brane AdS5 background dual to 4d CFT’s at finite temperature for operators of large scaling dimension. We find a formula that matches the expected structure of the OPE. It exhibits an exponentiation property, whose origin we explain. We also compute the first correction to the two-point function due to graviton emission, which encodes the proper time from the event horizon to the black hole singularity.

scholarly journals Gauged sigma-models with nonclosed 3-form and twisted Jacobi structures

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Athanasios Chatzistavrakidis ◽  
Grgur Šimunić
Keyword(s):  
Sigma Models ◽  
Sigma Model ◽  
Target Space ◽  
Two Dimensional ◽  
Courant Algebroids ◽  
Dirac Structures ◽  
Courant Algebroid ◽  
Abelian Case ◽  
Jacobi Manifolds ◽  
Jacobi Structure

Abstract We study aspects of two-dimensional nonlinear sigma models with Wess-Zumino term corresponding to a nonclosed 3-form, which may arise upon dimensional reduction in the target space. Our goal in this paper is twofold. In a first part, we investigate the conditions for consistent gauging of sigma models in the presence of a nonclosed 3-form. In the Abelian case, we find that the target of the gauged theory has the structure of a contact Courant algebroid, twisted by a 3-form and two 2-forms. Gauge invariance constrains the theory to (small) Dirac structures of the contact Courant algebroid. In the non-Abelian case, we draw a similar parallel between the gauged sigma model and certain transitive Courant algebroids and their corresponding Dirac structures. In the second part of the paper, we study two-dimensional sigma models related to Jacobi structures. The latter generalise Poisson and contact geometry in the presence of an additional vector field. We demonstrate that one can construct a sigma model whose gauge symmetry is controlled by a Jacobi structure, and moreover we twist the model by a 3-form. This construction is then the analogue of WZW-Poisson structures for Jacobi manifolds.

scholarly journals HETEROTIC T-DUALITY AND THE RENORMALIZATION GROUP

1999 ◽  
Vol 14 (14) ◽  
pp. 2257-2271 ◽  
Author(s):  
KASPER OLSEN ◽  
RICARDO SCHIAPPA
Keyword(s):  
Renormalization Group ◽  
Sigma Models ◽  
Sigma Model ◽  
Beta Function ◽  
Target Space ◽  
Loop Order ◽  
Duality Transformations ◽  
Duality Symmetry ◽  
The One ◽  
Renormalization Group Flows

We consider target space duality transformations for heterotic sigma models and strings away from renormalization group fixed points. By imposing certain consistency requirements between the T-duality symmetry and renormalization group flows, the one-loop gauge beta function is uniquely determined, without any diagram calculations. Classical T-duality symmetry is a valid quantum symmetry of the heterotic sigma model, severely constraining its renormalization flows at this one-loop order. The issue of heterotic anomalies and their cancellation is addressed from this duality constraining viewpoint.

scholarly journals GAUSS DECOMPOSITION, WAKIMOTO REALIZATION AND GAUGED WZNW MODELS

1994 ◽  
Vol 09 (11) ◽  
pp. 1009-1023
Author(s):  
H. ARFAEI ◽  
N. MOHAMMEDI
Keyword(s):  
Field Strength ◽  
Sigma Model ◽  
Target Space ◽  
Gauge Fields ◽  
Nonlinear Sigma Model ◽  
Model Interpretation ◽  
Gauss Decomposition ◽  
Wznw Model ◽  
Wakimoto Realization

The implications of gauging the Wess-Zumino-Novikov-Witten (WZNW) model using the Gauss decomposition of the group elements are explored. We show that, contrary to the standard gauging of WZNW models, this gauging is carried out by minimally coupling the gauge fields. We find that this gauging, in the case of gauging and Abelian vector subgroup, differs from the standard one by terms proportional to the field strength of the gauge fields. We prove that gauging an Abelian vector subgroup does not have a nonlinear sigma model interpretation. This is because the target-space metric resulting from the integration over the gauge fields is degenerate. We demonstrate, however, that this kind of gauging has a natural interpretation in terms of Wakimoto variables.

scholarly journals A Quantization Procedure of Fields Based on Geometric Langlands Correspondence

2009 ◽  
Vol 2009 ◽  
pp. 1-14
Author(s):  
Do Ngoc Diep
Keyword(s):  
Symmetry Group ◽  
Lie Algebra ◽  
Vector Bundles ◽  
Sigma Model ◽  
Fock Space ◽  
Loop Algebra ◽  
Target Space ◽  
Automorphic Representations ◽  
Langlands Correspondence ◽  
Geometric Langlands

We expose a new procedure of quantization of fields, based on the Geometric Langlands Correspondence. Starting from fields in the target space, we first reduce them to the case of fields on one-complex-variable target space, at the same time increasing the possible symmetry groupGL. Use the sigma model and momentum maps, we reduce the problem to a problem of quantization of trivial vector bundles with connection over the space dual to the Lie algebra of the symmetry groupGL. After that we quantize the vector bundles with connection over the coadjoint orbits of the symmetry groupGL. Use the electric-magnetic duality to pass to the Langlands dual Lie groupG. Therefore, we have some affine Kac-Moody loop algebra of meromorphic functions with values in Lie algebra=Lie(G). Use the construction of Fock space reprsentations to have representations of such affine loop algebra. And finally, we have the automorphic representations of the corresponding Langlands-dual Lie groupsG.

scholarly journals The nature of the gravitational vacuum

2019 ◽  
Vol 28 (14) ◽  
pp. 1944005
Author(s):  
Samir D. Mathur
Keyword(s):  
Black Hole ◽  
String Theory ◽  
Cosmological Constant ◽  
Mass Formula ◽  
Vacuum Energy ◽  
Planck Scale ◽  
Cosmological Constant Problem ◽  
Horizon Radius ◽  
Number Formula ◽  
Gravitational Vacuum

The vacuum must contain virtual fluctuations of black hole microstates for each mass [Formula: see text]. We observe that the expected suppression for [Formula: see text] is counteracted by the large number [Formula: see text] of such states. From string theory, we learn that these microstates are extended objects that are resistant to compression. We argue that recognizing this ‘virtual extended compression-resistant’ component of the gravitational vacuum is crucial for understanding gravitational physics. Remarkably, such virtual excitations have no significant effect for observable systems like stars, but they resolve two important problems: (a) gravitational collapse is halted outside the horizon radius, removing the information paradox, (b) spacetime acquires a ‘stiffness’ against the curving effects of vacuum energy; this ameliorates the cosmological constant problem posed by the existence of a planck scale [Formula: see text].

scholarly journals Analytic integrability for holographic duals with $$ J\overline{T} $$ deformations

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Dibakar Roychowdhury
Keyword(s):  
Phase Space ◽  
Finite Temperature ◽  
Sigma Model ◽  
Target Space ◽  
Variational Equations ◽  
Analytic Integrability ◽  
Holographic Duals ◽  
Space Dynamics ◽  
Classical Phase Space ◽  
Rules Set

Abstract We probe warped BTZ ×S3 geometry with various string solitons and explore the classical integrability criteria of the associated phase space configurations using Kovacic’s algorithm. We consider consistent truncation of the parent sigma model into one dimension and obtain the corresponding normal variational equations (NVE). Two specific examples have been considered where the sigma model is reduced over the subspace of the full target space geometry. In both examples, NVEs are found to possess Liouvillian form of solutions which ensures the classical integrability of the associated phase space dynamics. We address similar issues for the finite temperature counterpart of the duality, where we analyse the classical phase space of the string soliton probing warped BTZ black string geometry. Our analysis reveals a clear compatibility between normal variational equations and the rules set by the Kovacic’s criteria. This ensures the classical integrability of the parent sigma model for the finite temperature extension of the duality conjecture.

Sign in / Sign up

Export Citation Format

Share Document