11 research outputs found
Quantum folded string and integrability: from finite size effects to Konishi dimension
Using the algebraic curve approach we one-loop quantize the folded string
solution for the type IIB superstring in AdS(5)xS(5). We obtain an explicit
result valid for arbitrary values of its Lorentz spin S and R-charge J in terms
of integrals of elliptic functions. Then we consider the limit S ~ J ~ 1 and
derive the leading three coefficients of strong coupling expansion of short
operators. Notably, our result evaluated for the anomalous dimension of the
Konishi state gives 2\lambda^{1/4}-4+2/\lambda^{1/4}. This reproduces correctly
the values predicted numerically in arXiv:0906.4240. Furthermore we compare our
result using some new numerical data from the Y-system for another similar
state. We also revisited some of the large S computations using our methods. In
particular, we derive finite--size corrections to the anomalous dimension of
operators with small J in this limit.Comment: 20 pages, 1 figure; v2: references added, typos corrected; v3: major
improvement of the references; v4: Discussion of short operators is
restricted to the case n=1. This restriction does not affect the main results
of the pape
TBA-like equations and Casimir effect in (non-)perturbative AdS/CFT
We consider high spin, , long twist, , planar operators (asymptotic
Bethe Ansatz) of strong SYM. Precisely, we compute the minimal
anomalous dimensions for large 't Hooft coupling to the lowest order
of the (string) scaling variable with GKP string size . At the leading order ,
we can confirm the O(6) non-linear sigma model description for this bulk term,
without boundary term . Going further, we derive,
extending the O(6) regime, the exact effect of the size finiteness. In
particular, we compute, at all loops, the first Casimir correction (in terms of the infinite size O(6) NLSM), which reveals only one
massless mode (out of five), as predictable once the O(6) description has been
extended. Consequently, upon comparing with string theory expansion, at one
loop our findings agree for large twist, while reveal for negligible twist,
already at this order, the appearance of wrapping. At two loops, as well as for
next loops and orders, we can produce predictions, which may guide future
string computations.Comment: Version 2 with: new exact expression for the Casimir energy derived
(beyond the first two loops of the previous version); UV theory formulated
and analysed extensively in the Appendix C; origin of the O(6) NLSM
scattering clarified; typos correct and references adde
Integrable Wilson loops
The generalized quark-antiquark potential of N=4 supersymmetric Yang-Mills
theory on S^3 x R calculates the potential between a pair of heavy charged
particles separated by an arbitrary angle on S^3 and also an angle in flavor
space. It can be calculated by a Wilson loop following a prescribed path and
couplings, or after a conformal transformation, by a cusped Wilson loop in flat
space, hence also generalizing the usual concept of the cusp anomalous
dimension. In AdS_5 x S^5 this is calculated by an infinite open string. I
present here an open spin-chain model which calculates the spectrum of
excitations of such open strings. In the dual gauge theory these are cusped
Wilson loops with extra operator insertions at the cusp. The boundaries of the
spin-chain introduce a non-trivial reflection phase and break the bulk symmetry
down to a single copy of psu(2|2). The dependence on the two angles is captured
by the two embeddings of this algebra into \psu(2|2)^2, i.e., by a global
rotation. The exact answer to this problem is conjectured to be given by
solutions to a set of twisted boundary thermodynamic Bethe ansatz integral
equations. In particular the generalized quark-antiquark potential or cusp
anomalous dimension is recovered by calculating the ground state energy of the
minimal length spin-chain, with no sites. It gets contributions only from
virtual particles reflecting off the boundaries. I reproduce from this
calculation some known weak coupling perturtbative results.Comment: 40 pages, 11 figures; v2-some formulas corrected, results unchange