38 research outputs found
Yang-Baxter deformations, AdS/CFT, and twist-noncommutative gauge theory
We give an AdS/CFT interpretation to homogeneous Yang-Baxter deformations of
the AdS_5 x S^5 superstring as noncommutative deformations of the dual gauge
theory, going well beyond the canonical noncommutative case. These homogeneous
Yang-Baxter deformations can be of so-called abelian or jordanian type. While
abelian deformations have a clear interpretation in string theory and many
already had well understood gauge theory duals, jordanian deformations appear
novel on both counts. We discuss the symmetry structure of the deformed string
from the uniformizing perspective of Drinfeld twists and indicate that this
structure can be realized on the gauge theory side by considering theories on
various noncommutative spaces. We then conjecture that these are the gauge
theory duals of our strings, modulo subtleties involving singularities. We
support this conjecture by a brane construction for two jordanian examples,
corresponding to noncommutative spaces with [x^-,x^i] ~ x^i (i=1,2). We also
discuss kappa-Minkowski type deformations of AdS_5 x S^5, one of which may be
the gravity dual of gauge theory on spacelike kappa-Minkowski space.Comment: v5, published version up to formatting, 32 page
Fermionic reductions of the AdS4 x CP3 superstring
We discuss fermionic reductions of type IIA superstrings on AdS4 x CP3 in
relation to the conjectured AdS4/CFT3 duality. The superstring theory is
described by means of a coset model construction, which is classically
integrable. We discuss the global light-cone symmetries of the action and
related kappa-symmetry gauge choices, and also present the complete quartic
action in covariant form with respect to these. Further, we study integrable
(fermionic) reductions, in particular, a reduction yielding a quadratic action
of two complex fermions on the string world-sheet. Interestingly, this model
appears to be exactly the same as the corresponding integrable reduction found
in the AdS5 x S5 case.Comment: 24 pages, v3 as publishe
Quantum Spectral Curve for the eta-deformed AdS_5xS^5 superstring
The spectral problem for the superstring and
its dual planar maximally supersymmetric Yang-Mills theory can be efficiently
solved through a set of functional equations known as the quantum spectral
curve. We discuss how the same concepts apply to the -deformed superstring, an integrable deformation of the superstring with quantum group symmetry. This model can
be viewed as a trigonometric version of the
superstring, like the relation between the XXZ and XXX spin chains, or the
sausage and the sigma models for instance. We derive the quantum
spectral curve for the -deformed string by reformulating the
corresponding ground-state thermodynamic Bethe ansatz equations as an analytic
system, and map this to an analytic system which upon suitable gauge
fixing leads to a system -- the quantum spectral curve. We
then discuss constraints on the asymptotics of this system to single out
particular excited states. At the spectral level the -deformed string and
its quantum spectral curve interpolate between the superstring and a superstring on "mirror" ,
reflecting a more general relationship between the spectral and thermodynamic
data of the -deformed string. In particular, the spectral problem of the
mirror string, and the thermodynamics of the
undeformed string, are described by a second
rational limit of our trigonometric quantum spectral curve, distinct from the
regular undeformed limit.Comment: 32+37 pages; 6 figures. v2: added reference
Double Wick rotating Green-Schwarz strings
Via an appropriate field redefinition of the fermions, we find a set of
conditions under which light cone gauge fixed world sheet theories of strings
on two different backgrounds are related by a double Wick rotation. These
conditions take the form of a set of transformation laws for the background
fields, complementing a set of transformation laws for the metric and B field
we found previously with a set for the dilaton and RR fields, and are
compatible with the supergravity equations of motion. Our results prove that at
least to second order in fermions, the AdS_5 x S^5 mirror model which plays an
important role in the field of integrability in AdS/CFT, represents a string on
`mirror AdS_5 x S^5', the background that follows from our transformations. We
discuss analogous solutions for AdS_3 x S^3 x T^4 and AdS_2 x S^2 x T^6. The
main ingredient in our derivation is the light cone gauge fixed action for a
string on an (almost) completely generic background, which we explicitly derive
to second order in fermions.Comment: v2, updated discussion on target space interpretation, elaborated
discussion on minor points, content matches published version, 28 pages, 3
figure
Integrability of the AdS_5 x S^5 superstring and its deformations
This article reviews the application of integrability to the spectral problem
of strings on AdS_5 x S^5 and its deformations. We begin with a pedagogical
introduction to integrable field theories culminating in the description of
their finite-volume spectra through the thermodynamic Bethe ansatz. Next, we
apply these ideas to the AdS_5 x S^5 string and in later chapters discuss how
to account for particular integrable deformations. Through the AdS/CFT
correspondence this gives an exact description of anomalous scaling dimensions
of single trace operators in planar N=4 supersymmetry Yang-Mills theory, its
`orbifolds', and beta and gamma-deformed supersymmetric Yang-Mills theory. We
also touch upon some subtleties arising in these deformed theories.
Furthermore, we consider complex excited states (bound states) in the su(2)
sector and give their thermodynamic Bethe ansatz description. Finally we
discuss the thermodynamic Bethe ansatz for a quantum deformation of the AdS_5 x
S^5 superstring S-matrix, with close relations to among others Pohlmeyer
reduced string theory, and briefly indicate more recent developments in this
area.Comment: v3, published version, introduction slightly broadened, typos
corrected, updates to outlook and references. Review based on author's PhD
thesis, 214 pages, many figures. Partly based on arXiv:1009.4118,
arXiv:1103.5853, arXiv:1111.0564, arXiv:1201.1451, arXiv:1208.3478, and
arXiv:1210.818
Quadratic twist-noncommutative gauge theory
Studies of noncommutative gauge theory have mainly focused on noncommutative
spacetimes with constant noncommutative structure, with little known about
actions for noncommutative 4D Yang-Mills theory beyond this case. We construct
an action for Yang-Mills theory on a quadratically-noncommutative spacetime,
i.e. of quantum-plane type, obtained from a Drinfeld twist, with star-gauge
symmetry. Applied to supersymmetric Yang-Mills theory, this gives a candidate
AdS/CFT dual of string theory on a related deformation of AdSS,
which is expected to be integrable in the planar limit.Comment: v1, 6 pages letter format, no figure