QUANTUM BLACK HOLES, STRINGS AND σ-MODELS AT θ=π: HAWKING QUANTUM EVAPORATION AS WORLD-SHEET RG-FLOW

1991 ◽  
Vol 06 (36) ◽  
pp. 3297-3311 ◽  
Author(s):  
IAN I. KOGAN
Keyword(s):  
Black Holes ◽  
Renormalization Group ◽  
Fixed Points ◽  
Quantum Hall ◽  
Conformal Factor ◽  
Two Dimensional ◽  
Stable States ◽  
World Sheet ◽  
Final State ◽  
Quantum Evaporation

We discuss the quantum black holes and even more generally the problem of quantum horizons in string theory. A toy model for quantum horizon is the two-dimensional O(3) σ-model. Using the interpretation of time as zero mode of conformal factor of world-sheet metric (Liouville field) the possible equivalence between two-dimensional renormalization group equations and Hawking quantum evaporation formula is found. The infrared fixed points of two-dimensional renormalization group corresponds to final state of the quantum black hole. Using conjecture that such a fixed points are described by σ-models with θ=π we suggest the axionic black holes as possible candidates to final (meta)stable states of black holes. The corresponding renormalization group picture are similar to the quantum Hall effect.

scholarly journals Isotropic Lifshitz scaling in four dimensions

2020 ◽  
Vol 17 (04) ◽  
pp. 2050053 ◽  
Author(s):  
Dario Zappalà
Keyword(s):  
Renormalization Group ◽  
Fixed Points ◽  
Critical Dimension ◽  
Two Dimensional ◽  
Continuous Line ◽  
Scalar Theory ◽  
Functional Renormalization Group ◽  
Four Dimensions ◽  
Dimension Formula

The presence of isotropic Lifshitz points for a [Formula: see text]-symmetric scalar theory is investigated with the help of the Functional Renormalization Group. In particular, at the supposed lower critical dimension [Formula: see text], evidence for a continuous line of fixed points is found for the [Formula: see text] theory, and the observed structure presents clear similarities with the properties observed in the two-dimensional Berezinskii–Kosterlitz–Thouless phase.

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 Islands in linear dilaton black holes

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Georgios K. Karananas ◽  
Alex Kehagias ◽  
John Taskas
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Entanglement Entropy ◽  
Von Neumann Entropy ◽  
Two Dimensional ◽  
Extremal Case ◽  
Von Neumann ◽  
Dimensional Black Hole ◽  
Linear Dilaton ◽  
Linear Dilaton Black Hole

Abstract We derive a novel four-dimensional black hole with planar horizon that asymptotes to the linear dilaton background. The usual growth of its entanglement entropy before Page’s time is established. After that, emergent islands modify to a large extent the entropy, which becomes finite and is saturated by its Bekenstein-Hawking value in accordance with the finiteness of the von Neumann entropy of eternal black holes. We demonstrate that viewed from the string frame, our solution is the two-dimensional Witten black hole with two additional free bosons. We generalize our findings by considering a general class of linear dilaton black hole solutions at a generic point along the σ-model renormalization group (RG) equations. For those, we observe that the entanglement entropy is “running” i.e. it is changing along the RG flow with respect to the two-dimensional worldsheet length scale. At any fixed moment before Page’s time the aforementioned entropy increases towards the infrared (IR) domain, whereas the presence of islands leads the running entropy to decrease towards the IR at later times. Finally, we present a four-dimensional charged black hole that asymptotes to the linear dilaton background as well. We compute the associated entanglement entropy for the extremal case and we find that an island is needed in order for it to follow the Page curve.

scholarly journals Two-dimensional black holes in a higher derivative gravity and matrix model

2008 ◽  
Vol 794 (1-2) ◽  
pp. 28-45 ◽  
Author(s):  
Kwangho Hur ◽  
Seungjoon Hyun ◽  
Hongbin Kim ◽  
Sang-Heon Yi
Keyword(s):  
Black Holes ◽  
Matrix Model ◽  
Two Dimensional ◽  
Higher Derivative

PERTURBED W3 CONFORMAL THEORIES AND SPIN-4/3 PARAFERMIONIC COSET MODELS

1991 ◽  
Vol 06 (25) ◽  
pp. 2281-2287 ◽  
Author(s):  
R. B. MANN ◽  
H. B. ZHENG
Keyword(s):  
Renormalization Group ◽  
Fixed Points ◽  
Renormalization Group Flows ◽  
Coset Models

Renormalization group flows in W3, conformal theories are analyzed in relation to the ones in spin-4/3 parafermionic coset models and some of the operator content for new fixed points is identified.

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