J. High Energy Phys.

2006

DOI: 10.1088/1126-6708/2006/10/070

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The α′ stretched horizon in the heterotic string

Qasem Exirifard¹

Abstract: The linear α ′ corrections and the field redefinition ambiguities are studied for half-BPS singular backgrounds representing a wrapped fundamental string. It is showed that there exist schemes in which the inclusion of all the linear α ′ corrections converts these singular solutions to black holes with a regular horizon for which the modified Hawking-Bekenstein entropy is in agreement with the statistical entropy.

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Discussion2

-Charge Black Holes In D =1

Introduction1

Higher-order Corrections To Entropy Of 4-charge Black Hole1

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Cited by 23 publications

(17 citation statements)

References 85 publications

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“…Again, for extremal black holes one expects AdS 2 × S 2 near-horizon geometry (3.1) which in the present case is given by: One proceeds in the similar fashion as in section 4. As basically all the building blocks were given in [11,36] (where only α ′ -correction to the entropy was calculated), we shall just state the results. In this case the α ′ expansion is an expansion in 1/N W .…”

Section: -Charge Black Holes In D =mentioning

confidence: 99%

α′²-corrections to extremal dyonic black holes in heterotic string theory

¹

,

²

,

³

2008

J. High Energy Phys.

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We calculate α ′2 -corrections to the entropy of the 5-dimensional 3-charge and the 4-dimensional 4-charge large extremal black holes using the low energy effective action of the heterotic string theory. In the 4-dimensional case, our results are in agreement with the microscopic statistical entropy both for the BPS and the non-BPS black holes. In the more interesting 5-dimensional case, where the direct microscopic stringy description is still unknown, our results for the BPS black holes are in agreement with the results obtained from the action supplemented with R 2 -correction obtained by supersymmetric completion of the gravitational Chern-Simons term. This agreement does not extend to the non-BPS black holes, for which we propose a different expression for the entropy. We show that the new expression is supported by certain α ′3 -order calculations, and by the arguments based on the AdS/CFT correspondence. Contents 1. Introduction: Motivation and results 1 2. D = 6 heterotic effective action 4 3. Entropy function and its expansion 7 4. 3-charge black holes in D = 5 9 5. 4-charge black holes in D = 4 13 A. Identification of charges 14 B. Near-horizon solutions 15 B.1 D = 5 3-charge extremal black holes 16 B.2 D = 4 4-charge extremal black holes 16C. On contributions from α ′2 and higher order terms in the action 18 the limit of small string coupling constant g s (free string limit), which for nw ≫ 1 is given by 1 [7,8,9] S (BP S) stat = 2π nw(N W + 4) , n > 0 .( 1.1) For n < 0 the corresponding states are non-BPS with the statistical entropy given byNote that (1.1) and (1.2) are exact in α ′ . Now, when one increases g s , it has been argued that at some point these states become black holes. While in this regime string theory becomes highly nonperturbative, it is expected that one can use low energy effective action (at least for large black holes). Indeed, in the lowest order in α ′ , the solutions which describe extremal black holes with the two electric (n and w) and the two magnetic charges (N and W ) were explicitly constructed [10]. The near-horizon effective string coupling constant is proportional to 1/|nw|, which means that one can neglect string loops for nw ≫ 1. Also, the expansion in α ′ is equivalent to the expansion in 1/|N W |. The Bekenstein-Hawking entropy is S bh(0) = 2π |nwN W |, in agreement with (1.1) and (1.2). The α ′ -corrections to the entropies were calculated in [11], with the results again in agreement with (1.1) and (1.2). Surprising results were obtained when the following two types of R 2 -corrections in the effective action were taken: (i) the supersymmetrized gravitational Chern-Simons term [12], (ii) the Gauss-Bonnet term [13]. Both of these actions give the black hole entropy in the BPS case in the exact agreement with the statistical entropy (1.1), while they do not reproduce (1.2) in the non-BPS case. These results are surprising because the full effective action contains an infinite number of additional terms, for which there is no obvious reason to produce a canceling c...

“…Again, for extremal black holes one expects AdS 2 × S 2 near-horizon geometry (3.1) which in the present case is given by: One proceeds in the similar fashion as in section 4. As basically all the building blocks were given in [11,36] (where only α ′ -correction to the entropy was calculated), we shall just state the results. In this case the α ′ expansion is an expansion in 1/N W .…”

Section: -Charge Black Holes In D =mentioning

confidence: 99%

α′²-corrections to extremal dyonic black holes in heterotic string theory

¹

,

²

,

³

2008

J. High Energy Phys.

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We calculate α ′2 -corrections to the entropy of the 5-dimensional 3-charge and the 4-dimensional 4-charge large extremal black holes using the low energy effective action of the heterotic string theory. In the 4-dimensional case, our results are in agreement with the microscopic statistical entropy both for the BPS and the non-BPS black holes. In the more interesting 5-dimensional case, where the direct microscopic stringy description is still unknown, our results for the BPS black holes are in agreement with the results obtained from the action supplemented with R 2 -correction obtained by supersymmetric completion of the gravitational Chern-Simons term. This agreement does not extend to the non-BPS black holes, for which we propose a different expression for the entropy. We show that the new expression is supported by certain α ′3 -order calculations, and by the arguments based on the AdS/CFT correspondence. Contents 1. Introduction: Motivation and results 1 2. D = 6 heterotic effective action 4 3. Entropy function and its expansion 7 4. 3-charge black holes in D = 5 9 5. 4-charge black holes in D = 4 13 A. Identification of charges 14 B. Near-horizon solutions 15 B.1 D = 5 3-charge extremal black holes 16 B.2 D = 4 4-charge extremal black holes 16C. On contributions from α ′2 and higher order terms in the action 18 the limit of small string coupling constant g s (free string limit), which for nw ≫ 1 is given by 1 [7,8,9] S (BP S) stat = 2π nw(N W + 4) , n > 0 .( 1.1) For n < 0 the corresponding states are non-BPS with the statistical entropy given byNote that (1.1) and (1.2) are exact in α ′ . Now, when one increases g s , it has been argued that at some point these states become black holes. While in this regime string theory becomes highly nonperturbative, it is expected that one can use low energy effective action (at least for large black holes). Indeed, in the lowest order in α ′ , the solutions which describe extremal black holes with the two electric (n and w) and the two magnetic charges (N and W ) were explicitly constructed [10]. The near-horizon effective string coupling constant is proportional to 1/|nw|, which means that one can neglect string loops for nw ≫ 1. Also, the expansion in α ′ is equivalent to the expansion in 1/|N W |. The Bekenstein-Hawking entropy is S bh(0) = 2π |nwN W |, in agreement with (1.1) and (1.2). The α ′ -corrections to the entropies were calculated in [11], with the results again in agreement with (1.1) and (1.2). Surprising results were obtained when the following two types of R 2 -corrections in the effective action were taken: (i) the supersymmetrized gravitational Chern-Simons term [12], (ii) the Gauss-Bonnet term [13]. Both of these actions give the black hole entropy in the BPS case in the exact agreement with the statistical entropy (1.1), while they do not reproduce (1.2) in the non-BPS case. These results are surprising because the full effective action contains an infinite number of additional terms, for which there is no obvious reason to produce a canceling c...

“…Although at the beginning the corrections have mainly been studied for the supersymmetric black holes where the attractor mechanism [5] was observed, recently it was generalized to non-supersymmetric cases as well (for example see [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]).…”

Section: Introductionmentioning

confidence: 99%

OnR²corrections for 5D black holes

2007

J. High Energy Phys.

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We study higher order corrections to extremal black holes/black string in five dimensions. These higher order corrections are due to supersymmetric completion of R 2 term in five dimensions. By making use of the results we extend the notion of very special geometry when higher derivative terms are also taken into account. This can be used to make a connection between total bundle space of near horizon wrapped M2's and wrapped M5's in the presence of higher order corrections. We also show how the corrected geometry removes the singularity of a small black hole. 1 alishah@theory.ipm.ac.ir

“…We notice that the field redefinition ambiguities and scheme dependence for black hole entropy in heterotic string theory has been discussed extensively in [10], where the author pointed out that since Wald's formula was applied on the local horizon which was the exact solution of the truncated equations of motion then Wald's entropy depended on the field redefinition ambiguity parameters. However, this problem can be solved by requiring that the result obtained via the entropy function formalism should agree with the statistical entropy.…”

Section: Discussionmentioning

confidence: 99%

“…Similarly, the scheme dependence also exists in our case and we expect that it can also be resolved likely. However, we still do not have a clear idea about how to choose the proper scheme following [10] due to the lack of understanding the corrections to the entropy from a microscopic point of view. We hope to address this problem in our future work.…”

Section: Discussionmentioning

confidence: 99%

“…If we consider the Weyl tensor part only, i.e. the corrections to the effective action turn out to be 10) then the corrected entropy function is…”

Section: Higher-order Corrections To Entropy Of 4-charge Black Holementioning

confidence: 99%

See 1 more Smart Citation

Entropy function for 4-charge extremal black holes in type IIA superstring theory

¹

,

²

2006

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We calculate the entropy of 4-charge extremal black holes in Type IIA supersting theory by using Sen's entropy function method. Using the low energy effective actions in both 10D and 4D, we find precise agreements with the Bekenstein-Hawking entropy of the black hole. We also calculate the higher order corrections to the entropy and find that they depend on the exact form of the higher order corrections to the effective action.

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