Topological transitions in bubbling half-BPS Type IIB geometries with SO(4) x SO(4) symmetry can be decomposed into a sequence of n elementary transitions. The half-BPS solution that describes the elementary transition is seeded by a phase space distribution of fermions filling two diagonal quadrants. We study the geometry of this solution in some detail. We show that this solution can be interpreted as a time dependent geometry, interpolating between two asymptotic pp-waves in the far past and the far future. The singular solution at the transition can be resolved in two different ways, related by the particle-hole duality in the effective fermion description. Some universal features of the topology change are governed by two-dimensional Type 0B string theory, whose double scaling limit corresponds to the Penrose limit of AdS_5 x S5 at topological transition. In addition, we present the full class of geometries describing the vicinity of the most general localized classical singularity that can occur in this class of half-BPS bubbling geometries.

Alternative gauge choices for worldsheet supersymmetry can elucidate dynamical phenomena obscured in the usual superconformal gauge. In the particular example of the tachyonic E_8 heterotic string, we use a judicious gauge choice to show that the process of closed-string tachyon condensation can be understood in terms of a worldsheet super-Higgs effect. The worldsheet gravitino assimilates the goldstino and becomes a dynamical propagating field. Conformal, but not superconformal, invariance is maintained throughout.

Topological transitions in bubbling half-BPS Type IIB geometries with SO(4) x SO(4) symmetry can be decomposed into a sequence of n elementary transitions. The half-BPS solution that describes the elementary transition is seeded by a phase space distribution of fermions filling two diagonal quadrants. We study the geometry of this solution in some detail. We show that this solution can be interpreted as a time dependent geometry, interpolating between two asymptotic pp-waves in the far past and the far future. The singular solution at the transition can be resolved in two different ways, related by the particle-hole duality in the effective fermion description. Some universal features of the topology change are governed by two-dimensional Type 0B string theory, whose double scaling limit corresponds to the Penrose limit of AdS_5 x S^5 at topological transition. In addition, we present the full class of geometries describing the vicinity of the most general localized classical singularity that can occur in this class of half-BPS bubbling geometries.

Abstract. Noncritical M-theory in 2+1 dimensions has been defined as a double-scaling limit of a nonrelativistic Fermi liquid on a flat two-dimensional plane. Here we study this noncritical M-theory in the limit of high energies, analogous to the alpha' --> infinity limit of string theory. In the related case of two-dimensional Type 0A strings, it has been argued that the conformal alpha' --> infinity limit leads to AdS_2 with a propagating fermion whose mass is set by the value of the RR flux. Here we provide evidence that in the high-energy limit, the natural ground state of noncritical M-theory similarly describes the AdS_2 x S1 spacetime, with a massless propagating fermion. We argue that the spacetime effective theory in this background is captured by a topological higher-spin extension of conformal Chern-Simons gravity in 2+1 dimensions, consistently coupled to a massless Dirac field. Intriguingly, the two-dimensional plane populated by the original nonrelativistic fermions is essentially the twistor space associated with the symmetry group of the AdS_2 x S1 spacetime; thus, at least in the high-energy limit, noncritical M-theory can be nonperturbatively described as a "Fermi liquid on twistor space.''

We study the spacetime decay to nothing in string theory and M-theory. First we recall a nonsupersymmetric version of heterotic M-theory, in which bubbles of nothing -- connecting the two E_8 boundaries by a throat -- are expected to be nucleated. We argue that the fate of this system should be addressed at weak string coupling, where the nonperturbative instanton instability is expected to turn into a perturbative tachyonic one. We identify the unique string theory that could describe this process: The heterotic model with one E_8 gauge group and a singlet tachyon. We then use worldsheet methods to study the tachyon condensation in the NSR formulation of this model, and show that it induces a worldsheet super-Higgs effect. The main theme of our analysis is the possibility of making meaningful alternative gauge choices for worldsheet supersymmetry, in place of the conventional superconformal gauge. We show in a version of unitary gauge how the worldsheet gravitino assimilates the goldstino and becomes dynamical. This picture clarifies recent results of Hellerman and Swanson. We also present analogs of R_\xi gauges, and note the importance of logarithmic CFT in the context of tachyon condensation.

In this thesis we construct a family of topological quantum gravity theories with the goal of finding a regime in which these theories' localization equations are Perelman's celebrated Ricci flow equations. The natural setting for these theories is a nonrelativistic N = 2 superspace in which the spacetime is foliated by leaves of constant time. The basis for this construction is a "primitive" topological theory involving the spatial metric and its corresponding spatial diffeomorphism invariance, with N = 2 BRST symmetry. The algebra of the BRST charges is chosen so that the localization equations derived from a BRST-invariant action are flow equations and the couplings in the action are chosen so that these flow equations take the exact form of Hamilton's Ricci flow equations. Gauging spatial diffeomorphisms and foliation-preserving time reparametrizations (initially in two separate steps, but later in a single sweeping step) leads us to a set of geometric constraints that produce three distinct classes of field content in the BRST multiplets involved. Notably, the superpotential of the gauged theory is precisely Perelman's F-functional and the role of his dilaton is played by our nonrelativistic lapse function. Perelman's Ricci flow equations are then obtained as localization equations from the gauged theory in the same way as Hamilton's were obtained from the primitive theory (up to an interesting reframing), satisfying our goal.

In this thesis, we explore the intersection between relativistic quantum gravity and non-equilibrium physics. We demonstrate a scenario where non-equilibrium physics can provideimportant insights into quantum gravity by non-perturbatively proving a weak gravity con-jecture using entropic considerations. We take a different approach to extending stringtheory to describe scenarios where the universe is not assumed to be static and eternal byapplying the Schwinger-Keldysh technique to Large-N gauge theories. We use the correspon-dence between Large-N gauge theories and string theory to derive a universal structure thatworldsheets must follow out of equilibrium.

Some of the most fundamental questions in theoretical physics can be formulated as puzzles of naturalness, such as the cosmological constant problem and the Higgs mass hierarchy problem. In condensed matter physics, the interpretation of the linear scaling of resistivity with temperature in the strange metal phase of high-temperature superconductors also arises as a naturalness puzzle. In this thesis, we explore the landscape of naturalness in nonrelativistic quantum field theories that exhibit anisotropic scaling in space and time. Such theories are referred to as the ``Aristotelian quantum field theories." In the simple case with scalars, we find that the constant shift symmetry is extended to a shift by a polynomial in spatial coordinates, which protects the technical naturalness of modes with a higher order dispersion. This discovery leads to a generalization of the relativistic Coleman-Hohenberg-Mermin-Wagner (CHMW) theorem to multicritical cases in lower critical dimension. By breaking the polynomial shift symmetries in a hierarchy, we find novel cascading phenomena with large natural hierarchies between the scales at which the values of z change, leading to an evasion of the "no-go" consequences of the relativistic CHMW theorem. Based on these formal developments, we propose potential applications both to the Higgs mass hierarchy problem and to the problem of linear resistivity in strange metals. Finally, encouraged by these nonrelativistic surprises that already arise in simple systems with scalars, we move on to more complicated systems with gauge symmetries. We study the quantization of Horava gravity in 2+1 dimensions and compute the anomalous dimension of the cosmological constant at one loop. However, nonrelativistic naturalness in gravity is still largely unexplored. Whether or not such nonrelativsitic twists have any implications for important naturalness puzzles, such as the cosmological constant problem, remains as an intriguing question.

In this dissertation, we examine the holographic description of strongly-coupled quantum field theories with Lifshitz fixed points. After reviewing the standard dictionary of Lifshitz holography, we carry out the holographic renormalization procedure for two different bulk gravitational theories that support asymptotically Lifshitz spacetimes. The first bulk theory is relativistic gravity with a massive vector and the second is an anisotropic theory of gravity.

In the bulk theory of relativistic gravity with a massive vector, we find that the holographic counterterms induced near anisotropic infinity take the form of the action for Horava-Lifshitz (HL) gravity, with the appropriate value of the dynamical critical exponent z. In the particular case of 3 + 1 bulk dimensions and z = 2 asymptotic scaling near infinity, we find a logarithmic counterterm, related to anisotropic Weyl anomaly of the dual CFT, and show that this counterterm reproduces precisely the action of conformal gravity at a z = 2 Lifshitz point in 2 + 1 dimensions, which enjoys anisotropic local Weyl invariance. We find, however, that only one of two independent central charges appears in the anomaly.

We next argue that bulk HL gravity provides the minimal holographic dual for Lifshitz-type field theories with anisotropic scaling and dynamical exponent z. First we show that Lifshitz spacetimes are vacuum solutions of HL gravity, without the need for additional matter. Then we show that it reproduces the full structure of the z = 2 anisotropic Weyl anomaly in dual field theories in 2 + 1 dimensions, while its minimal relativistic gravity counterpart yields only one of two independent central charges in the anomaly.

Finally, we search for static asymptotically Lifshitz black hole solutions in HL gravity. In contrast to general relativity, we find that these static solutions do not have black hole horizons and instead contain naked singularities. In general, we argue that it is necessary to search for stationary (but non-static) black holes with universal horizons.