String stars in anti de Sitter space

We describe how to calculate the Hagedorn temperature of $$ \mathcal{N} $$ N = 4 SYM theory and type IIB superstring theory on AdS5 × S5 via the Quantum Spectral Curve (QSC) — providing further details on our previous letters [1] and [2]. We solve the QSC equations perturbatively at weak ‘t Hooft coupling λ up to seven-loop order and numerically at finite coupling, finding that the perturbative results can be expressed in terms of single-valued harmonic polylogarithms. Moreover, we generalize the QSC to describe the Hagedorn temperature in the presence of chemical potentials. Finally, we show that the Hagedorn temperature in certain deformations of $$ \mathcal{N} $$ N = 4 SYM theory (real-β and γi deformation) agrees with the one in $$ \mathcal{N} $$ N = 4 SYM theory at any value of λ.

Section: Jhep07(2022)136 1 Introductionsupporting

confidence: 53%

Section: Jhep07(2022)136mentioning

confidence: 99%

Section: Acknowledgmentsmentioning

confidence: 99%

“…We thank Juan Maldacena for sharing his calculation with us and for making us aware of the independent calculation[42] that appeared since.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Solving the Hagedorn temperature of AdS5/CFT4 via the Quantum Spectral Curve: chemical potentials and deformations

Harmark¹,

Wilhelm²

2022

“…Additionally, the author conjectured the existence of complex HP-like solutions with higher winding and momentum numbers which would explain the expected ramp-up in time of this variant in weakly-coupled string theories. An HP-like solution with an asymptotically AdS factor of the geometry was found in [28], its instability and a potential transition to a small black hole in AdS were also discussed. The authors of [29] found a family of HP-like solutions that asymptote to S 1 β × R 6 where β corresponds to the inverse Hagedorn temperature, and also identified worldsheet conformal field theories (CFTs) that describe them.…”

Section: Jhep10(2022)112mentioning

confidence: 98%

On the entropy of strings and branes

Brustein

Zigdon

2022

We show that the entropy of strings that wind around the Euclidean time circle is proportional to the Noether charge associated with translations along the T-dual time direction. We consider an effective target-space field theory which includes a large class of terms in the action with various modes, interactions and α′ corrections. The entropy and the Noether charge are shown to depend only on the values of fields at the boundary of space. The classical entropy, which is proportional to the inverse of Newton’s constant, is then calculated by evaluating the appropriate boundary term for various geometries with and without a horizon. We verify, in our framework, that for higher-curvature pure gravity theories, the Wald entropy of static neutral black hole solutions is equal to the entropy derived from the Gibbons-Hawking boundary term. We then proceed to discuss horizonless geometries which contain, due to the back-reaction of the strings and branes, a second boundary in addition to the asymptotic boundary. Near this “punctured” boundary, the time-time component of the metric and the derivatives of its logarithm approach zero. Assuming that there are such non-singular solutions, we identify the entropy of the strings and branes in this geometry with the entropy of the solution to all orders in α′. If the asymptotic region of an α′-corrected neutral black hole is connected through the bulk to a puncture, then the black hole entropy is equal to the entropy of the strings and branes. Later, we discuss configurations similar to the charged black p-brane solutions of Horowitz and Strominger, with the second boundary, and show that, to leading order in the α′ expansion, the classical entropy of the strings and branes is equal exactly to the Bekenstein-Hawking entropy. This result is extended to a configuration that asymptotes to AdS.

Hagedorn temperature from the thermal scalar in AdS and pp-wave backgrounds

Harmark

2024

We propose a thermal scalar equation of motion (EOM) that takes into account curvature corrections for backgrounds supported by Ramond-Ramond fluxes. This can be used to obtain the Hagedorn temperature for type II string theory on AdS and pp-wave backgrounds. For Ramond-Ramond flux supported pp-waves we show that the proposed thermal scalar EOM reproduces the leading curvature correction in the Hagedorn temperature equation obtained from the type II string theory spectrum. Furthermore, we use the thermal scalar EOM to obtain curvature corrections to the Hagedorn temperature for the AdS5 × S5 and AdS4 × ℂP3 backgrounds. These corrections match with strong coupling results of the integrable dual field theories, recently obtained by the Quantum Spectral Curve technique.