199 research outputs found
Nonrelativistic String Theory in Background Fields
Nonrelativistic string theory is a unitary, ultraviolet finite quantum
gravity theory with a nonrelativistic string spectrum. The vertex operators of
the worldsheet theory determine the spacetime geometry of nonrelativistic
string theory, known as the string Newton-Cartan geometry. We compute the Weyl
anomaly of the nonrelativistic string worldsheet sigma model describing strings
propagating in a string Newton-Cartan geometry, Kalb-Ramond and dilaton
background. We derive the equations of motion that dictate the backgrounds on
which nonrelativistic string theory can be consistently defined quantum
mechanically. The equations of motion we find from our study of the conformal
anomaly of the worldsheet theory are to nonrelativistic string theory what the
(super)gravity equations of motion are to relativistic string theory.Comment: 32 pages; v2: minor clarifications, fixed typos, references added;
v3: a reference adde
An Action for Extended String Newton-Cartan Gravity
We construct an action for four-dimensional extended string Newton-Cartan
gravity which is an extension of the string Newton-Cartan gravity that
underlies nonrelativistic string theory. The action can be obtained as a
nonrelativistic limit of the Einstein-Hilbert action in General Relativity
augmented with a term that contains an auxiliary two-form and one-form gauge
field that both have zero flux on-shell. The four-dimensional extended string
Newton-Cartan gravity is based on a central extension of the algebra that
underlies string Newton-Cartan gravity.
The construction is similar to the earlier construction of a
three-dimensional Chern-Simons action for extended Newton-Cartan gravity, which
is based on a central extension of the algebra that underlies Newton-Cartan
gravity. We show that this three-dimensional action is naturally obtained from
the four-dimensional action by a reduction over the spatial isometry direction
longitudinal to the string followed by a truncation of the extended string
Newton-Cartan gravity fields. Our construction can be seen as a special case of
the construction of an action for extended p-brane Newton-Cartan gravity in p+3
dimensions.Comment: 16 pages; v2: references added; v3: 18 pages, published versio
Multicritical Symmetry Breaking and Naturalness of Slow Nambu-Goldstone Bosons
We investigate spontaneous global symmetry breaking in the absence of Lorentz
invariance, and study technical Naturalness of Nambu-Goldstone (NG) modes whose
dispersion relation exhibits a hierarchy of multicritical phenomena with
Lifshitz scaling and dynamical exponents . For example, we find NG modes
with a technically natural quadratic dispersion relation which do not break
time reversal symmetry and are associated with a single broken symmetry
generator, not a pair. The mechanism is protected by an enhanced `polynomial
shift' symmetry in the free-field limit.Comment: 5 pages, 1 figure; v2: minor typos corrected, references adde
Anisotropic Compactification of Nonrelativistic M-Theory
We study a decoupling limit of M-theory where the three-form gauge potential
becomes critical. This limit leads to nonrelativistic M-theory coupled to a
non-Lorentzian spacetime geometry. Nonrelativistic M-theory is U-dual to
M-theory in the discrete light cone quantization, a non-perturbative approach
related to the Matrix theory description of M-theory. We focus on the
compactification of nonrelativistic M-theory over a two-torus that exhibits
anisotropic behaviors due to the foliation structure of the spacetime geometry.
We develop a frame covariant formalism of the toroidal geometry, which provides
a geometrical interpretation of the recently discovered polynomial realization
of SL(2,Z) duality in nonrelativistic type IIB superstring theory. We will show
that the nonrelativistic IIB string background fields transform as polynomials
of an effective Galilean "boost velocity" on the two-torus. As an application,
we construct an action principle describing a single M5-brane in
nonrelativistic M-theory and study its compactification over the anisotropic
two-torus. This procedure leads to a D3-brane action in nonrelativistic IIB
string theory that makes the SL(2,Z) invariance manifest in the polynomial
realization.Comment: 44 page
Nonrelativistic String Theory and T-Duality
Nonrelativistic string theory in flat spacetime is described by a
two-dimensional quantum field theory with a nonrelativistic global symmetry
acting on the worldsheet fields. Nonrelativistic string theory is unitary,
ultraviolet complete and has a string spectrum and spacetime S-matrix enjoying
nonrelativistic symmetry. The worldsheet theory of nonrelativistic string
theory is coupled to a curved spacetime background and to a Kalb-Ramond
two-form and dilaton field. The appropriate spacetime geometry for
nonrelativistic string theory is dubbed string Newton-Cartan geometry, which is
distinct from Riemannian geometry. This defines the sigma model of
nonrelativistic string theory describing strings propagating and interacting in
curved background fields. We also implement T-duality transformations in the
path integral of this sigma model and uncover the spacetime interpretation of
T-duality. We show that T-duality along the longitudinal direction of the
string Newton-Cartan geometry describes relativistic string theory on a
Lorentzian geometry with a compact lightlike isometry, which is otherwise only
defined by a subtle infinite boost limit. This relation provides a first
principles definition of string theory in the discrete light cone quantization
(DLCQ) in an arbitrary background, a quantization that appears in
nonperturbative approaches to quantum field theory and string/M-theory, such as
in Matrix theory. T-duality along a transverse direction of the string
Newton-Cartan geometry equates nonrelativistic string theory in two distinct,
T-dual backgrounds.Comment: 26 pages; v2: minor clarifications, a reference added; v3:
clarifications, references added, fixed typo
New Heat Kernel Method in Lifshitz Theories
We develop a new heat kernel method that is suited for a systematic study of
the renormalization group flow in Horava gravity (and in Lifshitz field
theories in general). This method maintains covariance at all stages of the
calculation, which is achieved by introducing a generalized Fourier transform
covariant with respect to the nonrelativistic background spacetime. As a first
test, we apply this method to compute the anisotropic Weyl anomaly for a
(2+1)-dimensional scalar field theory around a z=2 Lifshitz point and
corroborate the previously found result. We then proceed to general scalar
operators and evaluate their one-loop effective action. The covariant heat
kernel method that we develop also directly applies to operators with spin
structures in arbitrary dimensions.Comment: 47 pages, 1 figure; v2: appendix C updated, minor typos corrected,
references adde
Scalar Field Theories with Polynomial Shift Symmetries
We continue our study of naturalness in nonrelativistic QFTs of the Lifshitz
type, focusing on scalar fields that can play the role of Nambu-Goldstone (NG)
modes associated with spontaneous symmetry breaking. Such systems allow for an
extension of the constant shift symmetry to a shift by a polynomial of degree
in spatial coordinates. These "polynomial shift symmetries" in turn protect
the technical naturalness of modes with a higher-order dispersion relation, and
lead to a refinement of the proposed classification of infrared Gaussian fixed
points available to describe NG modes in nonrelativistic theories. Generic
interactions in such theories break the polynomial shift symmetry explicitly to
the constant shift. It is thus natural to ask: Given a Gaussian fixed point
with polynomial shift symmetry of degree , what are the lowest-dimension
operators that preserve this symmetry, and deform the theory into a
self-interacting scalar field theory with the shift symmetry of degree ? To
answer this (essentially cohomological) question, we develop a new
graph-theoretical technique, and use it to prove several classification
theorems. First, in the special case of (essentially equivalent to
Galileons), we reproduce the known Galileon -point invariants, and find
their novel interpretation in terms of graph theory, as an equal-weight sum
over all labeled trees with vertices. Then we extend the classification to
and find a whole host of new invariants, including those that represent
the most relevant (or least irrelevant) deformations of the corresponding
Gaussian fixed points, and we study their uniqueness.Comment: 70 pages. v2: minor clarifications, typos corrected, a reference
adde
- …