To go or not to go with the flow: Hawking radiation at strong coupling
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Springer
Received: April 17, 2020 Accepted: May 24, 2020 Published: June 16, 2020
Jorge E. Santos Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, U.K. Institute for Advanced Study, Princeton, NJ 08540, U.S.A.
E-mail: [email protected] Abstract: We construct the gravitational dual of a one-parameter class of states of strongly coupled SU(N ) N = 4 SYM at infinite N and asymptotic temperature T∞ , on a fixed Schwarzschild black hole background with temperature TBH . The resulting bulk geometry is of the flowing type and allow us to measure Hawking radiation at strong coupling. The outgoing Hawking flux is a function of the dimensionless ratio τ ≡ T∞ /TBH and appears to be non-monotonic in τ . At present, we have no field theory understanding for this behaviour. Keywords: AdS-CFT Correspondence, Black Holes, Nonperturbative Effects ArXiv ePrint: 2003.05454
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP06(2020)104
JHEP06(2020)104
To go or not to go with the flow: Hawking radiation at strong coupling
Contents 1
2 Constructing the holographic dual
3
3 The horizon and its properties
7
4 Extracting the holographic-stress energy tensor
9
5 Results
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6 Discussion
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A Convergence tests
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1
Introduction
Understanding the behaviour of Quantum Field Theories (QFTs) in curved spacetime is an important problem, not least because we know that the universe does contain regions of very large curvature. A key discovery was Hawking’s calculation demonstrating particle production in black hole backgrounds [1, 2]. These particles have a thermal spectrum, confirming that black holes should properly be thought of as thermodynamic objects. A general argument based on the Euclidean time formalism shows that for any QFT, an equilibrium state on a black hole background (the so-called Hartle-Hawking state) should be thermal [3]. However most of what is known about QFTs in curved spacetime comes from calculations involving free or weakly interacting theories. Little is known about the case when the QFT is strongly coupled. In fact, even in the weakly interacting regime there are interesting open puzzles, as for instance those reported in [4]. Gauge/Gravity Duality provides a new way of probing the behaviour of certain strongly coupled QFTs in curved backgrounds. In its most precise and well motivated form, it is the claim that Type IIB Superstring theory on AdS5 × S 5 is equivalent to N = 4 Super YangMills (SYM) theory on the (3 + 1) dimensional conformal boundary [5–8]. In the large N strong coupling limit of the boundary gauge theory, the bulk string theory becomes weakly coupled and the string length scale becomes small. In principle this should allow us to study quantum effects in the strongly coupled theory, such as Hawking radiation, by solving classical gravitational equations of motion in the bulk. This technique was explored in [9–12], and reviewed rather beautifully in [13]. In order to probe the Hawki
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