Spherical Branes

We construct new solutions of ten-dimensional supergravity with sixteen supercharges which describe the backreaction of D$p$-branes with spherical worldvolume. These solutions are holographically dual to the $(p+1)$-dimensional maximally supersymmetric Yang-Mills theory on $S^{p+1}$. The finite size of the sphere provides an IR cut-off for the gauge theory which is manifested in the supergravity solution as a smooth cap-off of the geometry. In the UV the size of the sphere plays no role and the backgrounds asymptote to the well-known supergravity solutions that describe the near-horizon limit of flat D$p$-branes. We compute the on-shell action of our spherical brane solutions and show that it is in agreement with recent supersymmetric localization results for the free energy of maximal SYM theory on $S^{p+1}$.Comment: 57 pages, 4 figures; v2: minor corrections, appendix adde

Unraveling the holomorphic twist: central charges

The holomorphic twist provides a powerful framework to study minimally protected sectors in supersymmetric quantum field theories. We investigate the algebraic structure underlying the holomorphic twist of N = 1 superconformal field theories in four dimensions. In particular, in holomorphically twisted theories the flavour and conformal symmetry algebras are enhanced to infinite-dimensional higher Kac Moody and higher Virasoro symmetry algebras respectively. We explicitly compute the binary and ternary λ-brackets and clarify their relation with the underlying infinite-dimensional symmetry algebra. Doing so we show that the central extensions of said symmetry algebras precisely encode the conformal anomalies a and c as well as the flavour central charges of the physical four-dimensional theory. This parallels the familiar story in two dimensions where the conformal anomaly c is encoded in the central extension of the Virasoro algebra

Symmetry breaking and consistent truncations from m5-branes wrapping a disc

We construct new supersymmetric solutions corresponding to M5-branes wrapped on a topological disc by turning on additional scalars in the background. The presence of such scalar fields breaks one of the U(1) isometries of the internal space, explicitly realising the breaking by the Stuckelberg mechanism observed previously. In addition, we construct a consistent truncation of maximal seven-dimensional gauged supergravity on the disc to five-dimensional Romans' SU (2) x U(1) gauged supergravity, allowing us to construct a plethora of new supergravity solutions corresponding to more general states in the dual SCFTs as well as solutions corresponding to M5-branes wrapping four-dimensional orbifolds

Symmetry Breaking and Consistent Truncations from M5-branes Wrapping a Disc

We construct new supersymmetric solutions corresponding to M5-branes wrapped on a topological disc by turning on additional scalars in the background. The presence of such scalar fields breaks one of the U(1) isometries of the internal space, explicitly realising the breaking by the Stuckelberg mechanism observed previously. In addition, we construct a consistent truncation of maximal seven-dimensional gauged supergravity on the disc to five-dimensional Romans' SU (2) x U(1) gauged supergravity, allowing us to construct a plethora of new supergravity solutions corresponding to more general states in the dual SCFTs as well as solutions corresponding to M5-branes wrapping four-dimensional orbifolds.Comment: 27 pages + appendices, 4 figure

Symmetry breaking and consistent truncations from M5-branes wrapping a disc

We construct new supersymmetric solutions corresponding to M5-branes wrapped on a topological disc by turning on additional scalars in the background. The presence of such scalar fields breaks one of the U(1) isometries of the internal space, explicitly realising the breaking by the Stückelberg mechanism observed previously. In addition, we construct a consistent truncation of maximal seven-dimensional gauged supergravity on the disc to five-dimensional Romans’ SU(2) × U(1) gauged supergravity, allowing us to construct a plethora of new supergravity solutions corresponding to more general states in the dual SCFTs as well as solutions corresponding to M5-branes wrapping four-dimensional orbifolds

Wrapped branes and punctured horizons

Publisher's version (útgefin grein)Large classes of AdSpsupergravity backgrounds describing the IR dynamicsofp-branes wrapped on a Riemann surface are determined by a solution to the Liouvilleequation. The regular solutions of this equation lead to the well-known wrapped branesupergravity solutions associated with the constant curvature metric on a compact Riemannsurface. We show that some singular solutions of the Liouville equation have a physicalinterpretation as explicit point-like brane sources on the Riemann surface. We uncover thedetails of this picture by focusing onN= 1theories of classSarising from M5-branes on apunctured Riemann surface. We present explicit AdS5solutions dual to these SCFTs andcheck the holographic duality by showing the non-trivial agreement of ’t Hooft anomalies.Peer Reviewe

Strange horizons

The gauge/gravity duality, also known as the AdS/CFT correspondence or holography, relates quantum field theories to theories of quantum gravity in one dimension higher. When one theory is strongly coupled, and therefore very difficult to study directly, the other one is weakly coupled. In this thesis, we will use this duality to study a variety of physical phenomena in strongly coupled quantum field theories by performing computations in their weakly coupled gravitational duals. After reviewing the gauge/gravity duality in the first part, we discuss various aspects of non-conformal holography in part II. We construct new solutions of ten-dimensional type II supergravity which describe the back-reaction of Dp-branes, for 1 =< p =< 6, with a spherical worldvolume. These solutions are holographically dual to maximally supersymmetric Yang-Mills (SYM) theory on a (p +1)-dimensional sphere, Sp+1. The finite size of the sphere provides a IR cut-off in the gauge theory, which is reflected in the dual geometry as a smooth cap-off. In the UV, the size of the sphere plays no role and our solutions asymptote to the well-known supergravity backgrounds describing the near-horizon limit of flat Dp-branes. Using these solutions we can holographically compute the free energy and 1/2-BPS Wilson loop vacuum expectation values in the dual gauge theory. Using supersymmetric localization, we can perform the same computation directly in planar maximal SYM theory on the (p+1)-sphere at strong coupling. We find excellent agreement between the two sets of results for all values of p. This constitutes a highly non-trivial precision test of holography in a non-conformal setting. In part III we study a class of AdSp solutions of type II supergravity which describe the IR dynamics of p-branes wrapped on a Riemann surface. Such solutions are classified by solutions of the Liouville equation. Regular solutions lead to well-known wrapped brane supergravity solutions with the constant curvature metric on the Riemann surface. We show that singular solutions of the Liouville also have a physical interpretation as explicit point-like brane sources on the Riemann surface. These supergravity solutions are dual to strongly coupled (p + 1)-dimensional conformal field theories obtained as the IR fixed point of a renormalization group flow across dimensions starting in p + 1 dimensions. These theories are strongly coupled and extremely hard to access using purely field theoretical methods. We test the details of our proposal by focusing on N = 1 superconformal field theories of class S, arising from M5-branes wrapped on a punctured Riemann surface. We present explicitly the dual AdS5 solutions and check the proposed duality by finding non-trivial agreement of the 't Hooft anomalies, the dimension of the conformal manifold and the conformal dimensions of various operators in the theory with their holographic duals.status: publishe

Wrapped branes and punctured horizons

status: publishe