Closed-String Tachyon Condensation and the Worldsheet Super-Higgs Effect

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.Comment: 4 pages; v2: typos corrected, a reference added; v3: final version, to appear in Phys. Rev. Lett. (abstract and intro modified for a broader audience

M-Theory Through the Looking Glass: Tachyon Condensation in the E_8 Heterotic String

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.Comment: 36 pages, 1 figur

Strings on AdS2 and the high-energy limit of noncritical M-theory

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.'&#39

Closed-String Tachyon Condensation and the Worldsheet Super-Higgs Effect

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

M-theory through the looking glass: Tachyon condensation in the E8 heterotic string

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

Deformations of Lifshitz holography

The simplest gravity duals for quantum critical theories with z=2 `Lifshitz' scale invariance admit a marginally relevant deformation. Generic black holes in the bulk describe the field theory with a dynamically generated momentum scale Lambda as well as finite temperature T. We describe the thermodynamics of these black holes in the quantum critical regime where T >> Lambda^2. The deformation changes the asymptotics of the spacetime mildly and leads to intricate UV sensitivities of the theory which we control perturbatively in Lambda^2/T.Comment: 1+27 pages, 12 figure

Noncritical M-Theory in 2+1 Dimensions as a Nonrelativistic Fermi Liquid

We claim that the dynamics of noncritical string theories in two dimensions is related to an underlying noncritical version of M-theory, which we define in terms of a double-scaled nonrelativistic Fermi liquid in 2+1 dimensions. After reproducing Type 0A and 0B string theories as solutions, we study the natural M-theory vacuum. The vacuum energy of this solution can be evaluated exactly, its form suggesting a duality to the Debye model of phonons in a melting solid, and a possible topological nature of the theory. The physical spacetime is emergent in this theory, only for states that admit a hydrodynamic description. Among the solutions of the hydrodynamic equations of motion for the Fermi surface, we find families describing the decay of one two-dimensional string theory into another via an intermediate M-theory phase.Comment: 47 pages, 1 figure; v2: typos corrected, references adde

Wilsonian Approach to Fluid/Gravity Duality

The problem of gravitational fluctuations confined inside a finite cutoff at radius $r=r_c$ outside the horizon in a general class of black hole geometries is considered. Consistent boundary conditions at both the cutoff surface and the horizon are found and the resulting modes analyzed. For general cutoff $r_c$ the dispersion relation is shown at long wavelengths to be that of a linearized Navier-Stokes fluid living on the cutoff surface. A cutoff-dependent line-integral formula for the diffusion constant $D(r_c)$ is derived. The dependence on $r_c$ is interpreted as renormalization group (RG) flow in the fluid. Taking the cutoff to infinity in an asymptotically AdS context, the formula for $D(\infty)$ reproduces as a special case well-known results derived using AdS/CFT. Taking the cutoff to the horizon, the effective speed of sound goes to infinity, the fluid becomes incompressible and the Navier-Stokes dispersion relation becomes exact. The resulting universal formula for the diffusion constant $D(horizon)$ reproduces old results from the membrane paradigm. Hence the old membrane paradigm results and new AdS/CFT results are related by RG flow. RG flow-invariance of the viscosity to entropy ratio $\eta /s$ is shown to follow from the first law of thermodynamics together with isentropy of radial evolution in classical gravity. The ratio is expected to run when quantum gravitational corrections are included.Comment: 34 pages, harvmac, clarified boundary conditio