18 research outputs found
Zooming in on AdS/CFT near a BPS Bound
Any -dimensional CFT with a flavor symmetry, a BPS bound and an
exactly marginal coupling admits a decoupling limit in which one zooms in on
the spectrum close to the bound. This limit is an In\"on\"u-Wigner contraction
of that leads to a relativistic algebra with a scaling
generator but no conformal generators. In 2D CFTs, Lorentz boosts are abelian
and by adding a second we find a contraction of two copies of
to two copies of , the 2-dimensional
centrally extended Poincar\'e algebra. We show that the bulk is described by a
novel non-Lorentzian geometry that we refer to as pseudo-Newton-Cartan
geometry. Both the Chern-Simons action on and the
entire phase space of asymptotically AdS spacetimes are well-behaved in the
corresponding limit if we fix the radial component for the connection.
With this choice, the resulting Newton-Cartan foliation structure is now
associated not with time, but with the emerging holographic direction. Since
the leaves of this foliation do not mix, the emergence of the holographic
direction is much simpler than in AdS holography. Furthermore, we show that
the asymptotic symmetry algebra of the limit theory consists of a left- and a
right-moving warped Virasoro algebra.Comment: 38 pages, v2: references added and typos corrected, v3: references
added, journal versio
Linear response of entanglement entropy from holography
For time-independent excited states in conformal field theories, the
entanglement entropy of small subsystems satisfies a `first law'-like relation,
in which the change in entanglement is proportional to the energy within the
entangling region. Such a law holds for time-dependent scenarios as long as the
state is perturbatively close to the vacuum, but is not expected otherwise. In
this paper we use holography to investigate the spread of entanglement entropy
for unitary evolutions of special physical interest, the so-called global
quenches. We model these using AdS-Vaidya geometries. We find that the first
law of entanglement is replaced by a linear response relation, in which the
energy density takes the role of the source and is integrated against a
time-dependent kernel with compact support. For adiabatic quenches the standard
first law is recovered, while for rapid quenches the linear response includes
an extra term that encodes the process of thermalization. This extra term has
properties that resemble a time-dependent `relative entropy'. We propose that
this quantity serves as a useful order parameter to characterize
far-from-equilibrium excited states. We illustrate our findings with concrete
examples, including generic power-law and periodically driven quenches.Comment: 31+3 pages, 8 figures; v2: typos fixed and references added; v3:
claims on universality sharpened (section 2.1), version to appear in JHE
Non-Riemannian isometries from double field theory
We explore the notion of isometries in non-Riemannian geometries. Such
geometries include and generalise the backgrounds of non-relativistic string
theory, and they can be naturally described using the formalism of double field
theory. Adopting this approach, we first solve the corresponding Killing
equations for constant flat non-Riemannian backgrounds and show that they admit
an infinite-dimensional algebra of isometries which includes a particular type
of supertranslations. These symmetries correspond to known worldsheet Noether
symmetries of the Gomis-Ooguri non-relativistic string, which we now interpret
as isometries of its non-Riemannian doubled background. We further consider the
extension to supersymmetric double field theory and show that the corresponding
Killing spinors can depend arbitrarily on the non-Riemannian directions,
leading to "supersupersymmetries" that square to supertranslations.Comment: 31+5 pages, v2: minor change
Spin Matrix theory string backgrounds and Penrose limits of AdS/CFT
Spin Matrix theory (SMT) limits provide a way to capture the dynamics of the
AdS/CFT correspondence near BPS bounds. On the string theory side, these limits
result in non-relativistic sigma models that can be interpreted as novel
non-relativistic strings. This SMT string theory couples to non-relativistic
-Galilean background geometries. In this paper, we explore the relation
between pp-wave backgrounds obtained from Penrose limits of AdS, and a new type of -Galilean backgrounds that we call flat-fluxed
(FF) backgrounds. These FF backgrounds are the simplest possible SMT string
backgrounds and correspond to free magnons from the spin chain perspective. We
provide a catalogue of the -Galilean backgrounds one obtains from SMT
limits of string theory on AdS and subsequently study large
charge limits of these geometries from which the FF backgrounds emerge. We show
that these limits are analogous to Penrose limits of AdS and
demonstrate that the large charge/Penrose limits commute with the SMT limits.
Finally, we point out that -Galilean backgrounds prescribe a symplectic
manifold for the transverse SMT string embedding fields. This is illustrated
with a Hamiltonian derivation for the SMT limit of a particle.Comment: 32 page
Galilean first-order formulation for the non-relativistic expansion of general relativity
We reformulate the Palatini action for general relativity (GR) in terms of
moving frames that exhibit local Galilean covariance in a large speed of light
expansion. For this, we express the action in terms of variables that are
adapted to a Galilean subgroup of the structure group of a
general frame bundle. This leads to a novel Palatini-type formulation of GR
that provides a natural starting point for a first-order non-relativistic
expansion. In doing so, we show how a comparison of Lorentzian and
Newton-Cartan metric-compatibility explains the appearance of torsion in the
non-relativistic expansion.Comment: 5+1 pages, v2: minor clarification
Longitudinal Galilean and Carrollian limits of non-relativistic strings
It is well known that one can take an infinite speed of light limit that
gives rise to non-relativistic strings with a relativistic worldsheet sigma
model but with a non-relativistic target space geometry. In this work we
systematically explore two further limits in which the worldsheet becomes
non-Lorentzian. The first gives rise to a Galilean string with a Galilean
structure on the worldsheet, extending previous work on Spin Matrix-related
string theory limits. The second is a completely novel limit leading to a
worldsheet theory with a Carrollian structure. We find the Nambu-Goto and
Polyakov formulations of both limits and explore gauge fixing choices.
Furthermore, we study in detail the case of the Galilean string for a class of
target space geometries that are related to Spin Matrix target space
geometries, for which the Nambu-Goto action (in static gauge) is quadratic in
the fields.Comment: 29+3 page
Relating non-relativistic string theories
Non-relativistic string theories promise to provide simpler theories of
quantum gravity as well as tractable limits of the AdS/CFT correspondence.
However, several apparently distinct non-relativistic string theories have been
constructed. In particular, one approach is to reduce a relativistic string
along a null isometry in target space. Another method is to perform an
appropriate large speed of light expansion of a relativistic string. Both of
the resulting non-relativistic string theories only have a well-defined
spectrum if they have nonzero winding along a longitudinal spatial direction.
In the presence of a Kalb--Ramond field, we show that these theories are
equivalent provided the latter direction is an isometry. Finally, we consider a
further limit of non-relativistic string theory that has proven useful in the
context of AdS/CFT (related to Spin Matrix Theory). In that case, the
worldsheet theory itself becomes non-relativistic and the dilaton coupling
vanishes.Comment: 23+5 pages, v2: added references and minor clarification
Exact approaches on the string worldsheet
We review different exact approaches to string theory. In the context of the
Green-Schwarz superstring, we discuss the action in curved backgrounds and its
supercoset formulation, with particular attention to superstring backgrounds of
the type supported by both Ramond-Ramond and
Neveu-Schwarz-Neveu-Schwarz fluxes. This is the basis for the discussion of
classical integrability, of worldsheet-scattering factorisation in the uniform
lightcone gauge, and eventually of the string spectrum through the mirror
thermodynamic Bethe ansatz, which for backgrounds was only derived and
analysed very recently. We then illustrate some aspects of the
Ramond-Neveu-Schwarz string, and introduce the formalism of
Berkovits-Vafa-Witten, which has seen very recent applications to
physics, which we also briefly review. Finally, we present the relation between
M-theory in the discrete lightcone quantisation and decoupling limits of string
theory that exhibit non-relativistic behaviours, highlighting the connection
with integrable deformations, as well as the relation between
spin-matrix theory and Landau-Lifshitz models. This review is based on lectures
given at the Young Researchers Integrability School and Workshop 2022 "Taming
the string worldsheet" at NORDITA, Stockholm.Comment: 283 pages; v2: references adde
Generalized Toda Theory from Six Dimensions and the Conifold
Recently, a physical derivation of the Alday-Gaiotto-Tachikawa correspondence
has been put forward. A crucial role is played by the complex Chern-Simons
theory arising in the 3d-3d correspondence, whose boundary modes lead to Toda
theory on a Riemann surface. We explore several features of this derivation and
subsequently argue that it can be extended to a generalization of the AGT
correspondence. The latter involves codimension two defects in six dimensions
that wrap the Riemann surface. We use a purely geometrical description of these
defects and find that the generalized AGT setup can be modeled in a pole region
using generalized conifolds. Furthermore, we argue that the ordinary conifold
clarifies several features of the derivation of the original AGT
correspondence.Comment: 27+2 pages, 3 figure