BPS Solutions of Six-Dimensional (1,0) Supergravity Coupled to Tensor Multiplets

We derive a general local form for supersymmetric solutions of six-dimensional (1,0) supergravity coupled to an arbitrary number of tensor multiplets. We consider some special cases in which the resulting equations can be solved explicitly. In particular we derive black string solutions and calculate their entropy. Upon reducing to five dimensions they yield spinning black hole solutions. We also discuss BPS pp-waves and black string solutions with traveling waves. Lastly, as an application, we study the attractor mechanism in this theory.Comment: 50 pages, no figures; v2: references added, updated discussion on the action of the theory; v3: updated references, minor typos correcte

Black Holes and (0,4) SCFTs from Type IIB on K3

We study the central charges and levels of 2d $\mathcal{N}=(0,4)$ superconformal field theories that are dual to four- and five-dimensional BPS black holes in compactifications of type IIB string theory on a K3 surface. They arise from wrapping a D3-brane on a curve $C$ inside K3 and have transverse space either an ALE or ALF space. These D3-branes have an AdS$_3 \times \mathrm{S}^3/ \Gamma$ near horizon geometry where $\Gamma$ is a discrete subgroup of $SU(2)$. We compute the central charges and levels of the 2d SCFTs both in the microscopic picture and from six-dimensional $\mathcal{N}=(2,0)$ supergravity. These quantities determine the black hole entropy via Cardy's formula. We find agreement between the microscopic and macroscopic computations. The contributions from one-loop quantum corrections to the macroscopic result are crucial for this matching.Comment: 36 pages; v2: published version, footnotes added, minor typos correcte

Anomalies of (0,4) SCFTs from F-theory

We study the macroscopics of 2d $\mathcal{N}=(0,4)$ SCFTs arising from F-theory constructions. The class of 2d SCFTs we consider live on black strings which are obtained by wrapping D3-branes on a curve in the base of a possibly singular elliptically fibered Calabi-Yau threefold. In addition, we allow the D3-branes to probe ALE or ALF spaces transversely. We compute anomaly coefficients of these SCFTs by determining Chern-Simons terms in the 3d action resulting from the reduction of 6d $\mathcal{N}=(1,0)$ supergravity on the compact space surrounding the black string. Essential contributions to these coefficients are from one-loop induced Chern-Simons terms arising from integrating out massive Kaluza-Klein modes.Comment: 38 pages, 1 figure; v2: references added, minor correction

Four-dimensional black hole entropy from F-theory

We study the central charges and levels of a two-dimensional $N=(0,4)$ superconformal field theory describing four-dimensional BPS black holes in F-theory. These arise from D3-branes wrapping a curve in the base of an elliptically fibered Calabi-Yau threefold times a circle, and probe a transverse Taub-NUT space. The near horizon geometry of these D3-branes is AdS$_3 \times \text{S}^3/\mathbb{Z}_m$, where $m$ is the NUT charge. Starting from a six-dimensional supergravity effective action we compute three-dimensional Chern-Simons terms to deduce the central charges and levels. We find that it is crucial to integrate out an infinite tower of massive Kaluza-Klein states on S$^3/\mathbb{Z}_m$ to match the expected microscopic results. The induced corrections turn out to contribute at leading order to the central charges and levels, which in turn determine the black hole entropy.Comment: 44 pages; v2: minor typos correcte

Twisted N = 1 SCFTs and their AdS3 duals

We study compactifications of an infinite family of four-dimensional N = 1 SCFTs on a Riemann surface in the presence of arbitrary background fluxes for global symmetries. The four-dimensional parent theories have holographic Sasaki-Einstein duals in type IIB string theory. We compute central charges and R-charges of baryonic operators in the resulting two-dimensional N = (0, 2) theories in three distinct ways: from the field theory side utilizing c-extremization, its recently discovered geometric dual formulation, and holographically using new AdS3 duals of two-dimensional field theories

Black Hole Entropy in String Theory

In the first part of the thesis we examine the entropy of black strings in compactifications of F-theory on an elliptically fibered Calabi-Yau threefold or of type IIB string theory on K3. The black strings arise as D3-branes wrapped on a curve in either the base of the Calabi-Yau threefold or in K3 and when compactified on an additional circle, they reduce to black holes. Macroscopically, they are described by solutions of 6d (1,0) supergravity coupled to tensor multiplets. We derive a general local form for supersymmetric solutions of this theory after which we consider several special cases in which the resulting equations can be solved explicitly. In particular, we derive expressions for the black string solutions we are interested in. In F-theory we consider black string solutions that have an asymptotically locally Euclidean (ALE) or asymptotically locally flat (ALF) space transversely. The black strings are dual to 2d (0,4) superconformal field theories (SCFTs) that arise as the IR fixed point of the compactified worldvolume theory of the branes. The entropy of the black strings is via the Cardy formula expressed in terms of the central charges and levels of the SCFT. We compute this data using the macroscopic black string solution. The central charges and levels correspond to coefficients of Chern-Simons terms in the 3d action resulting from the reduction of the 6d supergravity theory on the compact space surrounding the string. It turns out that to capture degrees of freedom living outside of the horizon one must perform this reduction at asymptotic infinity. In addition, one should include one-loop Chern-Simons terms arising from integrating out massive Kaluza-Klein modes. For the black strings considered we can only match with a microscopic computation when the transverse space is either flat or equal to Taub-NUT. Therefore, we also consider black strings probing ALE/ALF spaces transversely in compactifications of type IIB string theory on K3. We again compute the central charges and levels using the 6d supergravity theory. When the space transverse to the string is either ALE or Taub-NUT there is a complementary microscopic computation. We find a perfect matching to the macroscopic computations. In the last part of the thesis we change gears a little. We study compactifications of the four-dimensional Labc quiver gauge theories on a Riemann surface. We compute central charges and R-charges of baryonic operators in the resulting 2d (0,2) theories in three distinct ways: from the field theory side utilizing c-extremization, its recently discovered geometric dual formulation, and holographically using new AdS3 duals of two-dimensional field theories. The latter solutions can be thought of as the near-horizon geometry of black strings that are asymptotically AdS5 x Labc. Since the central charge is related to the entropy density of the strings, the matching we find between the supergravity and field theory sides can be viewed as a microscopic counting of the degrees of freedom of these strings

Black Hole Entropy in String Theory

In the first part of the thesis we examine the entropy of black strings in compactifications of F-theory on an elliptically fibered Calabi-Yau threefold or of type IIB string theory on K3. The black strings arise as D3-branes wrapped on a curve in either the base of the Calabi-Yau threefold or in K3 and when compactified on an additional circle, they reduce to black holes. Macroscopically, they are described by solutions of 6d (1,0) supergravity coupled to tensor multiplets. We derive a general local form for supersymmetric solutions of this theory after which we consider several special cases in which the resulting equations can be solved explicitly. In particular, we derive expressions for the black string solutions we are interested in. In F-theory we consider black string solutions that have an asymptotically locally Euclidean (ALE) or asymptotically locally flat (ALF) space transversely. The black strings are dual to 2d (0,4) superconformal field theories (SCFTs) that arise as the IR fixed point of the compactified worldvolume theory of the branes. The entropy of the black strings is via the Cardy formula expressed in terms of the central charges and levels of the SCFT. We compute this data using the macroscopic black string solution. The central charges and levels correspond to coefficients of Chern-Simons terms in the 3d action resulting from the reduction of the 6d supergravity theory on the compact space surrounding the string. It turns out that to capture degrees of freedom living outside of the horizon one must perform this reduction at asymptotic infinity. In addition, one should include one-loop Chern-Simons terms arising from integrating out massive Kaluza-Klein modes. For the black strings considered we can only match with a microscopic computation when the transverse space is either flat or equal to Taub-NUT. Therefore, we also consider black strings probing ALE/ALF spaces transversely in compactifications of type IIB string theory on K3. We again compute the central charges and levels using the 6d supergravity theory. When the space transverse to the string is either ALE or Taub-NUT there is a complementary microscopic computation. We find a perfect matching to the macroscopic computations. In the last part of the thesis we change gears a little. We study compactifications of the four-dimensional Labc quiver gauge theories on a Riemann surface. We compute central charges and R-charges of baryonic operators in the resulting 2d (0,2) theories in three distinct ways: from the field theory side utilizing c-extremization, its recently discovered geometric dual formulation, and holographically using new AdS3 duals of two-dimensional field theories. The latter solutions can be thought of as the near-horizon geometry of black strings that are asymptotically AdS5 x Labc. Since the central charge is related to the entropy density of the strings, the matching we find between the supergravity and field theory sides can be viewed as a microscopic counting of the degrees of freedom of these strings

BPS solutions of six-dimensional (1, 0) supergravity coupled to tensor multiplets

We derive a general local form for supersymmetric solutions of six-dimensional (1, 0) supergravity coupled to an arbitrary number of tensor multiplets. We consider some special cases in which the resulting equations can be solved explicitly. In particular we derive black string solutions and calculate their entropy. Upon reducing to five dimensions they yield spinning black hole solutions. We also discuss BPS pp-waves and black string solutions with traveling waves. Lastly, as an application, we study the attractor mechanism in this theory

Singularities in FLRW Spacetimes

We point out that past-incompleteness of geodesics in FLRW spacetimes does not necessarily imply that these spacetimes start from a singularity. Namely, if a test particle that follows such a trajectory has a non-vanishing velocity, its energy was super-Planckian at some time in the past if it kept following that geodesic. That indicates a breakdown of the particle's description, which is why we should not consider those trajectories for the definition of an initial singularity. When one only considers test particles that do not have this breakdown of their trajectory, it turns out that the only singular FLRW spacetimes are the ones that have a scale parameter that vanishes at some initial time