scholarly journals Equilibrium density matrices for the 2D black hole sigma models from an integrable spin chain

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Vladimir V. Bazhanov ◽  
Gleb A. Kotousov ◽  
Sergei L. Lukyanov
Keyword(s):  
Black Hole ◽  
Density Matrix ◽  
Sigma Models ◽  
Spin Chain ◽  
Sigma Model ◽  
Conformal Symmetry ◽  
Scaling Limit ◽  
Equilibrium Density ◽  
Modular Invariant ◽  
Integrable Spin

Abstract This work concerns the quantum Lorentzian and Euclidean black hole non-linear sigma models. For the Euclidean black hole sigma model an equilibrium density matrix is proposed, which reproduces the modular invariant partition function from the 2001 paper of Maldacena, Ooguri and Son. For the Lorentzian black hole sigma model, using its formulation as a gauged SL(2, ℝ) WZW model, we describe the linear and Hermitian structure of its space of states and also propose an expression for the equilibrium density matrix. Our analysis is guided by the results of the study of a certain critical, integrable spin chain. In the scaling limit, the latter exhibits the key features of the Lorentzian black hole sigma model including the same global symmetries, the same algebra of extended conformal symmetry and a continuous spectrum of conformal dimensions.

scholarly journals Integrable Spin Chain for theSL(2,R)/U(1)Black Hole Sigma Model

2012 ◽  
Vol 108 (8) ◽  
Author(s):  
Yacine Ikhlef ◽  
Jesper Lykke Jacobsen ◽  
Hubert Saleur
Keyword(s):  
Black Hole ◽  
Spin Chain ◽  
Sigma Model ◽  
Integrable Spin

scholarly journals Cosmology of linear Higgs-sigma models with conformal invariance

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Hyun Min Lee ◽  
Adriana G. Menkara
Keyword(s):  
Sigma Models ◽  
Sigma Model ◽  
Conformal Symmetry ◽  
Field Potential ◽  
Ultra Violet ◽  
Linear Sigma Model ◽  
Effective Theory ◽  
Vacuum Stability ◽  
The Standard Model ◽  
Linear Sigma Models

Abstract We consider general linear Higgs-sigma models as ultra-violet completions of the Higgs inflation. We introduce general higher curvature terms beyond Einstein gravity and recast them into a class of linear Higgs-sigma models in the scalar-dual formulation where conformal symmetry is manifest. Integrating out the sigma field in this class of linear sigma models, we obtain the same Higgs inflation Lagrangian of non-linear sigma model type in the effective theory. We show that the successful inflation for sigma field singles out the sigma-field potential derived from the R2 term and the tracker solution for dark energy at late times can be realized for the Rp+1 term with −1 < p < 0. We also discuss the implications of Higgs-sigma interactions for the inflation and the vacuum stability in the Standard Model.

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 A representation basis for the quantum integrable spin chain associated with the su(3) algebra

2016 ◽  
Vol 2016 (5) ◽  
Author(s):  
Kun Hao ◽  
Junpeng Cao ◽  
Guang-Liang Li ◽  
Wen-Li Yang ◽  
Kangjie Shi ◽  
...  
Keyword(s):  
Spin Chain ◽  
Integrable Spin

scholarly journals Fix the dual geometries of $$T\bar{T}$$ deformed CFT$$_2$$ and highly excited states of CFT$$_2$$

2020 ◽  
Vol 80 (12) ◽  
Author(s):  
Peng Wang ◽  
Houwen Wu ◽  
Haitang Yang
Keyword(s):  
Black Hole ◽  
Excited States ◽  
Conformal Symmetry ◽  
Propagation Speed ◽  
Conformally Flat ◽  
Btz Black Hole ◽  
Perfect Agreement ◽  
Conical Defect ◽  
Dual Geometries ◽  
Btz Metric

AbstractIn previous works, we have developed an approach to fix the leading behaviors of the pure AdS$$_3$$ 3 and BTZ black hole from the entanglement entropies of the free CFT$$_2$$ 2 and finite temperature CFT$$_2$$ 2 , respectively. We exclusively use holographic principle only and make no restriction about the bulk geometry, not only the kinematics but also the dynamics. In order to verify the universality and correctness of our method, in this paper, we apply it to the $$T\bar{T}$$ T T ¯ deformed CFT$$_2$$ 2 , which breaks the conformal symmetry. In terms of the physical arguments of the $$T\bar{T}$$ T T ¯ deformed CFT$$_2$$ 2 , the derived metric is a deformed BTZ black hole. The requirement that the CFT$$_2$$ 2 lives on a conformally flat boundary leads to $$r_{c}^{2}=\ 6R_{AdS}^{4}/(\pi c\mu )$$ r c 2 = 6 R AdS 4 / ( π c μ ) naturally, in perfect agreement with previous conjectures in literature. The energy spectum and propagation speed calculated with this deformed BTZ metric are the same as these derived from $$T\bar{T}$$ T T ¯ deformed CFT$$_2$$ 2 . We furthermore fix the dual geometry of highly excited states with our approach. The result contains the descriptions for the conical defect and BTZ black hole.

scholarly journals Hidden conformal symmetry of the Kerr black hole

2010 ◽  
Vol 82 (2) ◽  
Author(s):  
Alejandra Castro ◽  
Alexander Maloney ◽  
Andrew Strominger
Keyword(s):  
Black Hole ◽  
Conformal Symmetry ◽  
Kerr Black Hole

More on extracting information about the initial state from the black hole radiation

2018 ◽  
Vol 33 (19) ◽  
pp. 1850108
Author(s):  
Hossein Ghaforyan ◽  
Somayyeh Shoorvazi ◽  
Alireza Sepehri ◽  
Tooraj Ghaffary
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Density Matrix ◽  
Quantum Entanglement ◽  
Event Horizon ◽  
Initial State ◽  
Black Hole Radiation ◽  
Total Information ◽  
Quantum Treatment ◽  
Collapse Process

Recently, some authors showed that a classical collapse scenario ignores this richness of information in the resulting spectrum and a consistent quantum treatment of the entire collapse process might allow us to retrieve much more information from the spectrum of the final radiation. We confirm these results and show that by considering the quantum entanglement between metrics, we can uncover information of black holes. In our model, a density matrix is defined for the spaces, both inside and outside of the event horizon. These inside and outside spaces of black holes are obtained by tracing from a bigger space. An observer that lives in this big space can recover total information regarding the inside and outside of black hole.

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