218 research outputs found
First-principles derivation of the AdS/CFT Y-systems
We provide a first-principles, perturbative derivation of the AdS5/CFT4
Y-system that has been proposed to solve the spectrum problem of N=4 SYM. The
proof relies on the computation of quantum effects in the fusion of some loop
operators, namely the transfer matrices. More precisely we show that the
leading quantum corrections in the fusion of transfer matrices induce the
correct shifts of the spectral parameter in the T-system. As intermediate steps
we study UV divergences in line operators up to first order and compute the
fusion of line operators up to second order for the pure spinor string in
AdS5xS5. We also argue that the derivation can be easily extended to other
integrable models, some of which describe string theory on AdS4, AdS3 and AdS2
spacetimes.Comment: 45 pages, 5 figures; v2: minor additions, JHEP versio
Some mixed Hodge structure on l^2-cohomology of covering of K\"ahler manifolds
We give methods to compute l^2-cohomology groups of a covering manifolds
obtained by removing pullback of a (normal crossing) divisor to a covering of a
compact K\"ahler manifold. We prove that in suitable quotient categories, these
groups admit natural mixed Hodge structure whose graded pieces are given by
expected Gysin maps.Comment: 40 pages. This revised version will be published in Mathematische
Annale
Minimality of planes in normed spaces
We prove that a region in a two-dimensional affine subspace of a normed space
has the least 2-dimensional Hausdorff measure among all compact surfaces
with the same boundary. Furthermore, the 2-dimensional Hausdorff area density
admits a convex extension to . The proof is based on a (probably)
new inequality for the Euclidean area of a convex centrally-symmetric polygon.Comment: 10 pages, v2: minor changes according to referees' comments, to
appear in GAF
Tailoring Three-Point Functions and Integrability II. Weak/strong coupling match
We compute three-point functions of single trace operators in planar N=4 SYM.
We consider the limit where one of the operators is much smaller than the other
two. We find a precise match between weak and strong coupling in the
Frolov-Tseytlin classical limit for a very general class of classical
solutions. To achieve this match we clarify the issue of back-reaction and
identify precisely which three-point functions are captured by a classical
computation.Comment: 36 pages. v2: figure added, references adde
Quantum finite-size effects for dyonic magnons in the AdS_4 x CP^3
We compute quantum corrections to finite-size effects for various dyonic
giant magnons in the AdS_4 x CP^3 in two different approaches. The off-shell
algebraic curve method is used to quantize the classical string configurations
in semi-classical way and to compute the corrections to the string energies.
These results are compared with the F-term L\"uscher formula based on the
S-matrix of the AdS_4 / CFT_3. The fact that the two results match exactly
provides another stringent test for the all-loop integrability conjecture and
the exact S-matrix based on it.Comment: 21 pages, No figures, corrected typos, added some reference
Strings on Semisymmetric Superspaces
Several string backgrounds which arise in the AdS/CFT correspondence are
described by integrable sigma-models. Their target space is always a Z(4)
supercoset (a semi-symmetric superspace). Here we list all semi-symmetric
cosets which have zero beta function and central charge c<=26 at one loop in
perturbation theory.Comment: 25 pages, 1 figur
On the worldsheet theory of the type IIA AdS(4) x CP(3) superstring
We perform a detailed study of the type IIA superstring in AdS(4) x CP(3).
After introducing suitable bosonic light-cone and fermionic kappa worldsheet
gauges we derive the pure boson and fermion SU(2|2) x U(1) covariant light-cone
Hamiltonian up to quartic order in fields.
As a first application of our derivation we calculate energy shifts for
string configurations in a closed fermionic subsector and successfully match
these with a set of light-cone Bethe equations. We then turn to investigate the
mismatch between the degrees of freedom of scattering states and oscillatory
string modes. Since only light string modes appear as fundamental Bethe roots
in the scattering theory, the physical role of the remaining massive
oscillators is rather unclear. By continuing a line of research initiated by
Zarembo, we shed light on this question by calculating quantum corrections for
the propagators of the bosonic massive fields. We show that, once loop
corrections are incorporated, the massive coordinates dissolve in a continuum
state of two light particles.Comment: 40 pages, 2 figures. v3: Minor clarifications made and reference list
updated. Published version
Strings in AdS_4 x CP^3: finite size spectrum vs. Bethe Ansatz
We compute the first curvature corrections to the spectrum of light-cone
gauge type IIA string theory that arise in the expansion of about a plane-wave limit. The resulting spectrum is shown to
match precisely, both in magnitude and degeneration that of the corresponding
solutions of the all-loop Gromov--Vieira Bethe Ansatz. The one-loop dispersion
relation correction is calculated for all the single oscillator states of the
theory, with the level matching condition lifted. It is shown to have all
logarithmic divergences cancelled and to leave only a finite exponentially
suppressed contribution, as shown earlier for light bosons. We argue that there
is no ambiguity in the choice of the regularization for the self-energy sum,
since the regularization applied is the only one preserving unitarity.
Interaction matrices in the full degenerate two-oscillator sector are
calculated and the spectrum of all two light magnon oscillators is completely
determined. The same finite-size corrections, at the order 1/J, where is
the length of the chain, in the two-magnon sector are calculated from the all
loop Bethe Ansatz. The corrections obtained by the two completely different
methods coincide up to the fourth order in . We
conjecture that the equivalence extends to all orders in and to
higher orders in 1/J.Comment: 32 pages. Published version; journal reference adde
Scattering of Giant Magnons in CP^3
We study classical scattering phase of CP^2 dyonic giant magnons in R_t x
CP^3. We construct two-soliton solutions explicitly by the dressing method.
Using these solutions, we compute the classical time delays for the scattering
of giant magnons, and compare them to boundstate S-matrix elements derived from
the conjectured AdS_4/CFT_3 S-matrix by Ahn and Nepomechie in the strong
coupling limit. Our result is consistent with the conjectured S-matrix. The
dyonic solutions play an essential role in revealing the polarization
dependence of scattering phase.Comment: 29 pages; v2: minor corrections; v3: minor corrections, references
added ; v4: minor corrections ; v5: minor corrections based on the published
versio
Finite-gap equations for strings on AdS_3 x S^3 x T^4 with mixed 3-form flux
We study superstrings on AdS_3 x S^3 x T^4 supported by a combination of
Ramond-Ramond and Neveu-Schwarz-Neveu-Schwarz three form fluxes, and construct
a set of finite-gap equations that describe the classical string spectrum.
Using the recently proposed all-loop S-matrix we write down the all-loop Bethe
ansatz equations for the massive sector. In the thermodynamic limit the Bethe
ansatz reproduces the finite-gap equations. As part of this derivation we
propose expressions for the leading order dressing phases. These phases differ
from the well-known Arutyunov-Frolov-Staudacher phase that appears in the pure
Ramond-Ramond case. We also consider the one-loop quantization of the algebraic
curve and determine the one-loop corrections to the dressing phases. Finally we
consider some classical string solutions including finite size giant magnons
and circular strings.Comment: 44 pages, 3 figures. v2: references and a discussion about
perturbative results adde
- …