A
bstract
We study reflected entropy as a mixed state correlation measure in black hole evaporation. As a measure for bipartite mixed states, reflected entropy can be computed between black hole and ...radiation, radiation and radiation, and even black hole and black hole. We compute reflected entropy curves in three different models: 3-side wormhole model, End-of-the-World (EOW) brane model in three dimensions and two-dimensional eternal black hole plus CFT model. For 3-side wormhole model, we find that reflected entropy is dual to island cross section. The reflected entropy between radiation and black hole increases at early time and then decreases to zero, similar to Page curve, but with a later transition time. The reflected entropy between radiation and radiation first increases and then saturates. For the EOW brane model, similar behaviors of reflected entropy are found.
We propose a quantum extremal surface for reflected entropy, which we call quantum extremal cross section. In the eternal black hole plus CFT model, we find a generalized formula for reflected entropy with island cross section as its area term by considering the right half as the canonical purification of the left. Interestingly, the reflected entropy curve between the left black hole and the left radiation is nothing but the Page curve. We also find that reflected entropy between the left black hole and the right black hole decreases and goes to zero at late time. The reflected entropy between radiation and radiation increases at early time and saturates at late time.
A
bstract
We propose defect extremal surface as the holographic counterpart of boundary quantum extremal surface. The defect extremal surface is defined by minimizing the Ryu-Takayanagi surface ...corrected by the defect theory. This is particularly interesting when the RT surface crosses or terminates on the defect. In a simple set up of AdS/BCFT, we find that the defect extremal surface formula gives precisely the same results of the boundary quantum extremal surface. We provide a decomposition procedure of an AdS bulk with a defect brane to see clearly how quantum extremal surface formula emerges from a brane world system with gravity glued to a flat space quantum field theory.
A
bstract
Defect extremal surface (DES) is defined by minimizing the Ryu-Takayanagi surface corrected by the quantum theory localized on the defect, which is useful when the RT surface crosses or ...terminates on the defect. Based on the decomposition procedure of an AdS bulk with a defect brane, proposed in 69, we derive Page curve in a time dependent set up of AdS
3
/BCFT
2
, and find that the result from island formula agrees with defect extremal surface formula precisely. We then extend the study to higher dimensions and find that the entropy computed from bulk defect extremal surface is generally less than that from island formula in boundary low energy effective theory, which implies that the UV completion of island formula gives a smaller entropy.
A
bstract
We introduce a new class of quantum and classical correlation measures by generalizing the reflected entropy to multipartite states. We define the new measures for quantum systems in one ...spatial dimension. For quantum systems having gravity duals, we show that the holographic duals of these new measures are various types of minimal surfaces consist of different entanglement wedge cross sections. One special generalized reflected entropy is ∆
R
, with the holographic dual proportional to the so called multipartite entanglement wedge cross section ∆
W
defined before. We then perform a large
c
computation of ∆
R
and find evidence to support ∆
R
= 2∆
W
. This shows another candidate ∆
R
as the dual of 2∆
W
and also supports our holographic conjecture of the new class of generalized reflected entropies.
On small black holes in string theory Balthazar, Bruno; Chu, Jinwei; Kutasov, David
The journal of high energy physics,
03/2024, Volume:
2024, Issue:
3
Journal Article
Peer reviewed
Open access
A
bstract
We discuss the worldsheet sigma-model whose target space is the
d
+1 dimensional Euclidean Schwarzschild black hole. We argue that in the limit where the Hawking temperature of the black ...hole,
T
, approaches the Hagedorn temperature,
T
H
, it can be described in terms of a generalized version of the Horowitz-Polchinski effective theory. For
d
≥ 6, where the Horowitz-Polchinski EFT
1
,
2
does not have suitable solutions, the modified effective Lagrangian allows one to study the black hole CFT in an expansion in powers of
d
− 6 and
T
H
−
T
. At
T
=
T
H
, the sigma model is non-trivial for all
d
> 6. It exhibits an enhanced SU(2) symmetry, and is described by a non-abelian Thirring model with a radially dependent coupling. The resulting picture connects naturally to the results of
3
–
5
, that relate Schwarzschild black holes in flat spacetime at large
d
to the two dimensional black hole. We also discuss an analogous open string system, in which the black hole is replaced by a system of two separated D-branes connected by a throat. In this system, the asymptotic separation of the branes plays the role of the inverse temperature. At the critical separation, the system is described by a Kondo-type model, which again exhibits an enhanced SU(2) symmetry. At large
d
, the brane system gives rise to the hairpin brane
6
.
A
bstract
In perturbative string theory, one is generally interested in asymptotic observables, such as the S-matrix in flat spacetime, and boundary correlation functions in anti-de Sitter spacetime. ...However, there are backgrounds in which such observables do not exist. We study examples of such backgrounds in 1 + 1 dimensional string theory. In these examples, the Liouville wall accelerates and can become spacelike in the past and/or future. When that happens, the corresponding null infinity, at which the standard scattering states are defined, is shielded by the Liouville wall. We compute scattering and particle production amplitudes in these backgrounds in the region in parameter space where the wall remains timelike, and discuss the continuation of this picture to the spacelike regime. We also discuss the physics from the point of view of the dynamics of free fermions in backgrounds with a time-dependent Fermi surface.
In AdS/CFT, we introduce a robust method for computing n -point gluon Mellin amplitudes, applicable in various spacetime dimensions. Using the Mellin transform and a recursive algorithm, we ...efficiently calculate tree-level gluon amplitudes. Our approach simplifies the representation of higher-point amplitudes, eliminating the need for complicated integrations. Crucially, the resulting amplitudes closely mirror those in flat space, allowing a straightforward dictionary between the two settings circumventing explicit calculations. Published by the American Physical Society 2024
We investigate the embedding formalism in conjunction with the Mellin transform to determine tree-level gluon amplitudes in AdS / CFT . Detailed computations of three to five-point correlators are ...conducted, ultimately distilling what were previously complex results for five-point correlators into a more succinct and comprehensible form. We then proceed to derive a recursion relation applicable to a specific class of n -point gluon amplitudes. This relation is instrumental in systematically constructing amplitudes for a range of topologies. We illustrate its efficacy by specifically computing six to eight-point functions. Despite the complexity encountered in the intermediate steps of the recursion, the higher-point correlator is succinctly expressed as a polynomial in boundary coordinates, upon which a specific differential operator acts. Remarkably, we observe that these amplitudes strikingly mirror their counterparts in flat space, traditionally computed using standard Feynman rules. This intriguing similarity has led us to propose a novel dictionary: comprehensive rules that bridge AdS Mellin amplitudes with flat-space gluon amplitudes. Published by the American Physical Society 2024
We investigate the embedding formalism in conjunction with the Mellin
transform to determine tree-level gluon amplitudes in AdS/CFT. Detailed
computations of three to five-point correlators are ...conducted, ultimately
distilling what were previously complex results for five-point correlators into
a more succinct and comprehensible form. We then proceed to derive a recursion
relation applicable to a specific class of $n$-point gluon amplitudes. This
relation is instrumental in systematically constructing amplitudes for a range
of topologies. We illustrate its efficacy by specifically computing six to
eight-point functions. Despite the complexity encountered in the intermediate
steps of the recursion, the higher-point correlator is succinctly expressed as
a polynomial in boundary coordinates, upon which a specific differential
operator acts. Remarkably, we observe that these amplitudes strikingly mirror
their counterparts in flat space, traditionally computed using standard Feynman
rules. This intriguing similarity has led us to propose a novel dictionary:
comprehensive rules that bridge AdS Mellin amplitudes with flat-space gluon
amplitudes.
In AdS/CFT, we introduce a robust method for computing $n$-point gluon Mellin
amplitudes, applicable in various spacetime dimensions. Using the Mellin
transform and a recursive algorithm, we ...efficiently calculate tree-level gluon
amplitudes. Our approach simplifies the representation of higher-point
amplitudes, eliminating the need for complicated integrations. Crucially, the
resulting amplitudes closely mirror those in flat space, allowing a
straightforward dictionary between the two settings circumventing explicit
calculations.
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