Effective field theory for closed strings near the Hagedorn temperature

We calculate the entropy of an asymptotically Schwarzschild black hole, using an effective field theory of winding modes in type II string theory. In Euclidean signature, the geometry of the black hole contains a thermal cycle which shrinks towards the horizon. The light excitations thus include, in addition to the metric and the dilaton, also the winding modes around this cycle. The winding modes condense in the near-horizon region and source the geometry of the thermal cycle. Using the effective field theory action and standard thermodynamic relations, we show that the entropy, which is also sourced by the winding modes condensate, is exactly equal to the Bekenstein-Hawking entropy of the black hole. We then discuss some properties of the winding mode condensate and end with an application of our method to an asymptotically linear-dilaton black hole.

show abstract

“…The term proportional to e 2σ in I 1 , reproduces a string S-matrix element [36] to leading order in the string coupling.…”

Section: Actionmentioning

confidence: 85%

“…(2.1). Based on the analysis in [36], we expect that when interactions are taken into account, the mass-squared of the winding modes in this region is actually small and positive.…”

Section: Some Properties Of the Winding-mode Condensate Profilementioning

confidence: 99%

Black hole entropy sourced by string winding condensate

Brustein

Zigdon

2021

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Note that the R 0 − R c scaling of the ϕ|χ| 2 interaction term is the same as that of the |χ| 4 term [22,39,40], which we ignored in the effective action above. But due to the l s /l ads scaling we have |χ| 4 ϕ|χ| 2 , and the approximation is still consistent.…”

Section: Evaporation To Gasmentioning

confidence: 99%

String Stars in Anti de Sitter Space

Urbach

2022

Preprint

View full text Add to dashboard Cite

We study the 'string star' saddle, also known as the Horowitz-Polchinski solution, in the middle of d + 1 dimensional thermal AdS space. We show that there's a regime of temperatures in which the saddle is very similar to the flat space solution found by Horowitz and Polchinski. This saddle is hypothetically connected at lower temperatures to the small AdS black hole saddle. We also study, numerically and analytically, how the solutions are changed due to the AdS geometry for higher temperatures. Specifically, we describe how the solution joins with the thermal gas phase, and find the leading correction to the Hagedorn temperature due to the AdS curvature. Finally, we study the thermodynamic instabilities of the solution and argue for a Gregory-Laflamme-like instability whenever extra dimensions are present at the AdS curvature scale.

show abstract

“…Recently, several papers were written about winding condensates. We calculated the coefficient of the interaction term between a radion and two winding modes by a string S-matrix computation for type II and the bosonic string in [19]. An additional interaction, the quartic interaction between four winding modes, was similarly computed in [19] for the bosonic string theory and type II superstring theory.…”

Section: Jhep10(2022)112mentioning

confidence: 99%

“…We calculated the coefficient of the interaction term between a radion and two winding modes by a string S-matrix computation for type II and the bosonic string in [19]. An additional interaction, the quartic interaction between four winding modes, was similarly computed in [19] for the bosonic string theory and type II superstring theory. A related calculation appeared in [20], and in [21], the same interactions were calculated for the Heterotic string.…”

Section: Jhep10(2022)112mentioning

confidence: 99%

On the entropy of strings and branes

Brustein

Zigdon

2022

J. High Energ. Phys.

View full text Add to dashboard Cite

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.

show abstract

Effective field theory for closed strings near the Hagedorn temperature

Cited by 9 publications

References 46 publications

Black hole entropy sourced by string winding condensate

Black hole entropy sourced by string winding condensate

String Stars in Anti de Sitter Space

On the entropy of strings and branes

Contact Info

Product

Resources

About