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Time warps

Steven S. Gubser

TL;DR

The paper investigates time warp geometries—asymmetrically warped extra dimensions with no bulk entropy or temperature—within a five-dimensional gravity–scalar model, demonstrating an AdS$_5$-like bulk where the coordinate speed of light varies from IR to UV and can be faster near the boundary. It analyzes the resulting Green's functions and unparticle phase space, showing how time-warp effects render the unparticle spectral measure momentum-dependent via a factor $W(k)$ and introduce UV timelike constraints that modify decay kinematics. To realize a four-dimensional graviton in this setup, it explores Planck-brane constructions that necessarily violate the null energy condition, and shows that a negative (wrong-sign) Einstein-Hilbert term on the brane can yield an IR-massless graviton, albeit with potential energy- or frequency-dependent issues. The work discusses phenomenological implications, including possible Lorentz-violating signals confined to a dual unparticle sector detectable at colliders, while highlighting significant theoretical challenges such as stability, NEC considerations, and embedding in a full string theory framework.

Abstract

I reconsider asymmetrically warped compactifications, in which time and space have different warp factors. I call such compactifications time warps if the bulk geometry has neither entropy nor temperature. I provide an example starting from an asymptotically AdS_5 spacetime where the speed of light, measured in a fixed coordinate system, is larger near the boundary than it is deep in the interior. This example follows the general plan of earlier work on superconducting black holes. To obtain a normalizable, four-dimensional graviton, one can introduce a Planck brane whose action includes a wrong-sign Einstein-Hilbert term. The equation of state of the Planck brane has w < -1, which is a violation of the null energy condition. I show, in an almost dimension-independent fashion, that such a violation must occur in a static time warp geometry. Time warps of the type I describe provide an extra-dimensional description of boost invariance as an emergent symmetry in the infrared. High-energy violations of Lorentz symmetry, if confined to a strongly coupled unparticle sector dual to the time warp geometry, might manifest themselves through unusual kinematic constraints. As an example, I explain how modifications of unparticle phase space would affect the decay of a heavy particle into a light visible sector particle plus unparticle stuff.

Time warps

TL;DR

The paper investigates time warp geometries—asymmetrically warped extra dimensions with no bulk entropy or temperature—within a five-dimensional gravity–scalar model, demonstrating an AdS-like bulk where the coordinate speed of light varies from IR to UV and can be faster near the boundary. It analyzes the resulting Green's functions and unparticle phase space, showing how time-warp effects render the unparticle spectral measure momentum-dependent via a factor and introduce UV timelike constraints that modify decay kinematics. To realize a four-dimensional graviton in this setup, it explores Planck-brane constructions that necessarily violate the null energy condition, and shows that a negative (wrong-sign) Einstein-Hilbert term on the brane can yield an IR-massless graviton, albeit with potential energy- or frequency-dependent issues. The work discusses phenomenological implications, including possible Lorentz-violating signals confined to a dual unparticle sector detectable at colliders, while highlighting significant theoretical challenges such as stability, NEC considerations, and embedding in a full string theory framework.

Abstract

I reconsider asymmetrically warped compactifications, in which time and space have different warp factors. I call such compactifications time warps if the bulk geometry has neither entropy nor temperature. I provide an example starting from an asymptotically AdS_5 spacetime where the speed of light, measured in a fixed coordinate system, is larger near the boundary than it is deep in the interior. This example follows the general plan of earlier work on superconducting black holes. To obtain a normalizable, four-dimensional graviton, one can introduce a Planck brane whose action includes a wrong-sign Einstein-Hilbert term. The equation of state of the Planck brane has w < -1, which is a violation of the null energy condition. I show, in an almost dimension-independent fashion, that such a violation must occur in a static time warp geometry. Time warps of the type I describe provide an extra-dimensional description of boost invariance as an emergent symmetry in the infrared. High-energy violations of Lorentz symmetry, if confined to a strongly coupled unparticle sector dual to the time warp geometry, might manifest themselves through unusual kinematic constraints. As an example, I explain how modifications of unparticle phase space would affect the decay of a heavy particle into a light visible sector particle plus unparticle stuff.

Paper Structure

This paper contains 9 sections, 78 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Solutions in the bulk
  3. Green's functions and unparticles
  4. Spectral measure and unparticle phase space
  5. Time warp modification of unparticle phase space
  6. The Planck brane
  7. Gravitons
  8. Discussion
  9. More on two-point correlators

Figures (3)

  • Figure 1: (Color online.) A time warp geometry for the choice of parameters (\ref{['ExampleParameters']}), in the gauge $B=0$. Solid colored curves are from numerics; dashed black curves are infrared asymptotics; and dotted black curves are ultraviolet asymptotics.
  • Figure 2: (Color online.) The phase space ratio $W(k)$ defined in (\ref{['WarpRatio']}), for values of parameters discussed in the main text. The vertical green line shows where UV-null momenta lie.
  • Figure 3: (Color online.) The distribution of energies $E_u$ for the $u$ quark in the process $t \to u + {\cal U}$, where the unparticle stuff has infrared dimension $\Delta_\phi^{\rm IR} = 2.98$ and the time warp modifications are from the factor $W(k)$ plotted in figure \ref{['WMOD']}. Different curves come from different choices of the dimensionless parameter $m_t L$. Each curve is normalized to have unit area under it.