133 research outputs found
Quantum Landau-Lifshitz model at four loops: 1/J and 1/J^2 corrections to BMN energies
In a previous paper (hep-th/0510080) the effective Landau-Lifshitz (LL)
Lagrangians in the SU(2) sector coming from string theory and gauge theory have
been found to three loops in the effective expansion parameter
. In this paper we continue this study and find the
effective Landau-Lifshitz Lagrangians to four loops. We extend to four-loops
the computations of 1/J and corrections to BMN
energies done in hep-th/0510080 to three-loops. We compare these corrections
obtained from quantum ``gauge-theory'' LL action with the corrections obtained
from the conjectured Bethe ansatz for the long range spin chain representing
perturbative {large } \NN=4 Super Yang-Mills in the SU(2) sector and find
perfect matching to four loops . We compare also the 1/J and
corrections obtained from quantum ``string-theory'' LL action with
those obtained from the "quantum string" Bethe ansatz and again find perfect
matching to four-loops.Comment: 22 pages, references adde
Quantum corrections to energy of short spinning string in AdS5
Motivated by desire to shed light on the strong coupling behaviour of
anomalous dimensions of "short" gauge theory operators we consider the famous
example of folded spinning string in AdS_5 in the limit of small semiclassical
spin parameter \S = S/sqrt[lambda]. In this limit the string becomes short and
is moving in a near-flat central region of AdS_5. Its energy scales with spin
as E = sqrt[2 S] [ a_0 + a_1 S + a_2 S^2 + ...]. We explicitly compute the
leading 1-loop quantum AdS_5 x S^5 superstring corrections to the short-string
limit coefficients a_0 and a_1 and show, in particular, that a_1 receives a
contribution containing \zeta(3).Comment: 27 pages; v2: comments and appendix B about regularization ambiguity
added; v3,4: minor corrections; v5: treatment of fermionic contribution
corrected, a new appendix and a note adde
Matching the circular Wilson loop with dual open string solution at 1-loop in strong coupling
We compute the 1-loop correction to the effective action for the string
solution in AdS_5 x S^5 dual to the circular Wilson loop. More generically, the
method we use can be applied whenever the two dimensional spectral problem
factorizes, to regularize and define the fluctuation determinants in terms of
solutions of one-dimensional differential equations. A such it can be applied
to non-homogeneous solutions both for open and closed strings and to various
boundary conditions. In the case of the circular Wilson loop, we obtain, for
the 1-loop partition function a result which up to a factor of two matches the
expectation from the exact gauge theory computation. The discrepancy can be
attributed to an overall constant in the string partition function coming from
the normalization of zero modes, which we have not fixed.Comment: 32 pages; v2: typos corrected, acknowledgments added; v3: minor
corrections, references adde
Semiclassical rigid strings with two spins in AdS_5
Semiclassical spinning string states in AdS_5 are, in general, characterised
by the three SO(2,4) conserved charges: the energy E and the two spins S_1 and
S_2. We discuss several examples of explicit classical solutions for rigid
closed strings of (bended) circular shape with two non-zero spins. In
particular, we identify a solution that should represent a state that has
minimal energy for large values of the two equal spins. Similarly to the spiky
string in AdS_3, in the large spin limit this string develops long "arcs" that
stretch towards the boundary of AdS_5. This allows the string to increase the
spin while having the energy growing only logarithmically with S=S_1 +S_2. The
large spin asymptotics of such solutions is effectively controlled by their
near-boundary parts which, as in the spiky string case, happen to be SO(2,4)
equivalent to segments of the straight folded spinning string. As a result, the
coefficient of the \log S term in the string energy should be given, up to an
overall 3/2 coefficient, by the same universal scaling function (cusp anomaly)
as in the folded string case, to all orders in the inverse string tension or
strong-coupling expansion.Comment: 34 pages, 9 figure
Spinning strings in AdS_5 x S^5: one-loop correction to energy in SL(2) sector
We consider a circular string with spin in wrapped around big
circle of and carrying also momentum . The corresponding N=4 SYM
operator belongs to the SL(2) sector, i.e. has tr structure. The
leading large term in its 1-loop anomalous dimension can be computed using
Bethe ansatz for the SL(2) spin chain and was previously found to match the
leading term in the classical string energy. The string solution is stable at
large , and the Lagrangian for string fluctuations has constant
coefficients, so that the 1-loop string correction to the energy is given
simply by the sum of characteristic frequencies. Curiously, we find that the
leading term in the zero-mode part of is the same as a 1/J correction to
the one-loop anomalous dimension on the gauge theory (spin chain) side that was
found in hep-th/0410105. However, the contribution of non-zero string modes
does not vanish. We also discuss the ``fast string'' expansion of the classical
string action which coincides with the coherent state action of the SL(2) spin
chain at the first order in \l, and extend this expansion to higher orders
clarifying the role of the winding number.Comment: 31 pages, 1 figure, latex; v3: minor changes and correction
Strong-coupling expansion of cusp anomaly and gluon amplitudes from quantum open strings in AdS_5 x S^5
An important ``observable'' of planar N=4 SYM theory is the scaling function
f(lambda) that appears in the anomalous dimension of large spin twist 2
operators and also in the cusp anomaly of light-like Wilson loops. The
non-trivial relation between the anomalous dimension and the Wilson
interpretations of f(lambda) is well-understood on the perturbative gauge
theory side of the AdS/CFT duality. In the first part of this paper we present
the dual string-theory counterpart of this relation, to all orders in
lambda^(-1/2) expansion. As a check, we explicitly compute the leading 1-loop
string sigma model correction to the cusp Wilson loop, reproducing the same
subleading coefficient in f(lambda) as found earlier in the spinning closed
string case. The same function f(lambda) appears also in the resummed form of
the 4-gluon amplitude as discussed at weak coupling by Bern, Dixon and Smirnov
and recently found at the leading order at strong coupling by Alday and
Maldacena (AM). Here we attempt to extend this approach to subleading order in
lambda^(-1/2) by computing the IR singular part of 1-loop string correction to
the corresponding T-dual Wilson loop. We discuss explicitly the 1-cusp case and
comment on apparent problems with the dimensional regularization proposal of AM
when directly applied order by order in strong coupling (inverse string
tension) expansion.Comment: 35 pages. v2: minor corrections, references adde
Spiky strings in AdS_3 x S^1 and their AdS-pp-wave limits
We study a class of classical solutions for closed strings moving in AdS_3 x
S^1 part of AdS_5 x S^5 with energy E and spin S in AdS_3 and angular momentum
J and winding m in S^1. They have rigid shape with n spikes in AdS_3. We find
that when J or m are non-zero, the spikes do not end in cusps. We consider in
detail a special large n limit in which S ~ n^2, J ~ n, i.e. S >> J >> 1, with
(E+S)/ n^2, (E-S)/ n, J/n, m/n staying finite. In that limit the spiky spinning
string approaches the boundary of AdS_5. We show that the corresponding
solution can be interpreted as describing a periodic-spike string moving in
AdS_3 --pp-wave x S^1 background. The resulting expression for the string
energy should represent a strong-coupling prediction for anomalous dimension of
a class of dual gauge theory states in a particular thermodynamic limit of the
SL(2) spin chain.Comment: 34 pages, 4 figures; v2: references added; v3: typos correcte
BPS and non-BPS states in a supersymmetric Landau-Ginzburg theory
We analyze the spectrum of the N=(2,2) supersymmetric Landau-Ginzburg theory
in two dimensions with superpotential W=X^{n+2}-lambda X^2. We find the full
BPS spectrum of this theory by exploiting the direct connection between the UV
and IR limits of the theory. The computation utilizes results from the
Picard-Lefschetz theory of singularities and its extension to boundary
singularities. The additional fact that this theory is integrable requires that
the BPS states do not close under scattering. This observation fixes the masses
of non-BPS states as well.Comment: 27 pages, 12 figure
Structure of large spin expansion of anomalous dimensions at strong coupling
The anomalous dimensions of planar N = 4 SYM theory operators like tr (ΦD S + Φ) expanded in large spin S have the asymptotics γ = f ln S + f c + 1 S (f 11 ln S + f 10 ) + ··· ,where f (the universal scaling function or cusp anomaly), f c and f mn are given by power series in the ’t Hooft coupling λ . The subleading coefficients appear to be related by the so-called functional relation and parity (reciprocity) property of the function expressing γ in terms of the conformal spin of the collinear group. Here we study the structure of such large spin expansion at strong coupling via AdS/CFT, i.e. by using the dual description in terms of folded spinning string in AdS 5 . The large spin expansion of the classical string energy happens to have exactly the same structure as that of γ in the perturbative gauge theory. Moreover, the functional relation and the reciprocity constraints on the coefficients are also satisfied. We compute the leading string 1-loop corrections to the coefficients f c , f 11 , f 10 and verify the functional/reciprocity relations at subleading 1 √ λ order. This provides a strong indication that these relations hold not only in weak coupling (gauge-theory) but also in strong coupling (string-theory) perturbative expansions
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