17 research outputs found
On string integrability. A journey through the two-dimensional hidden symmetries in the AdS/CFT dualities
One of the main topics in the modern String Theory are the AdS/CFT dualities.
Proving such conjectures is extremely difficult since the gauge and string
theory perturbative regimes do not overlap. In this perspective, the discovery
of infinitely many conserved charges, i.e. the integrability, in the planar
AdS/CFT has allowed us to reach immense progresses in understanding and
confirming the duality. We review the fundamental concepts and properties of
integrability in two-dimensional sigma-models and in the AdS/CFT context. The
first part is focused on the AdS_5/CFT_4 duality, especially the classical and
quantum integrability of the type IIB superstring on AdS_5 x S^5 are discussed
in both pure spinor and Green-Schwarz formulations. The second part is
dedicated to the AdS_4/CFT_3 duality with particular attention to the type IIA
superstring on AdS_4 x CP^3 and its integrability. This review is based on a
shortened and revised version of the author's PhD thesis, discussed at Uppsala
University in September 2009.Comment: 116 pages, 11 figures, to be published in Advances in High Energy
Physics, Special Issue on ''Gauge/String Duality'
Aspects of quantum integrability for pure spinor superstring in AdS(5)xS(5)
We consider the monodromy matrix for the pure spinor IIB superstring on
at leading order at strong coupling, in particular its
variation under an infinitesimal and continuous deformation of the contour.
Such variation is equivalent to the insertion of a local operator. Demanding
the BRST-closure for such an operator rules out its existence, implying that
the monodromy matrix remains contour-independent at the first order in
perturbation theory. Furthermore we explicitly compute the field strength
corresponding to the flat connections up to leading order and directly check
that it is free from logarithmic divergences. The absence of anomaly in the
coordinate transformation of the monodromy matrix and the UV-finiteness of the
curvature tensor finally imply the integrability of the pure spinor superstring
at the first order.Comment: 44 pages; 4 figure
Quantized Strings and Instantons in Holography
We study worldsheet instantons in holographic type IIA backgrounds directly
in string theory. The first background is a dimensional reduction of
AdS and is dual to the maximally supersymmetric Yang-Mills theory
on . The second background is AdS dual to ABJM in
the type IIA limit. We compute the one-loop partition function of the
fundamental string in these backgrounds and show that the result is in exact
agreement with field theory predictions. We argue that for higher rank
instantons, the string partition function takes a product form of the single
instanton partition function times the contribution of two orbifolds on the
worldsheet. We determine the orbifold factor to be where is the
instanton rank. With this result, we reproduce the series of non-perturbative
corrections in to the planar free energy. When studying the
worldsheet instanton partition function on , we encounter twelve
fermionic and twelve bosonic zero modes. By deforming the ABJM theory, the
zero-modes are lifted and consequently the tower of worldsheet instantons can
be evaluated and matched to known results in the QFT. As a by-product, we
determine a series of higher rank instanton corrections to the free energy of
the mass-deformed and orbifolded ABJ(M) theory.Comment: 35 pages. v2: Minor correction
Finite-size corrections in the SU(2) x SU(2) sector of type IIA string theory on AdS_4 x CP^3
We consider finite-size corrections in the SU(2) x SU(2) sector of type IIA
string theory on AdS_4 x CP^3, which is the string dual of the recently
constructed N=6 superconformal Chern-Simons theory of Aharony, Bergman,
Jafferis and Maldacena (ABJM theory). The string states we consider are in the
R x S^2 x S^2 subspace of AdS_4 x CP^3 with an angular momentum J on CP^3 being
large. We compute the finite-size corrections using two different methods, one
is to consider curvature corrections to the Penrose limit giving an expansion
in 1/J, the other by considering a low energy expansion in lambda'=lambda/J^2
of the string theory sigma-model, lambda being the 't Hooft coupling of the
dual ABJM theory. For both methods there are interesting issues to deal with.
In the near-pp-wave method there is a 1/\sqrt{J} interaction term for which we
use zeta-function regularization in order to compute the 1/J correction to the
energy. For the low energy sigma-model expansion we have to take into account a
non-trivial coupling to a non-dynamical transverse direction. We find agreement
between the two methods. At order lambda' and lambda'^2, for small lambda', our
results are analogous to the ones for the SU(2) sector in type IIB string
theory on AdS_5 x S^5. Instead at order lambda'^3 there are interactions
between the two two-spheres. We compare our results with the recently proposed
all-loop Bethe ansatz of Gromov and Vieira and find agreement.Comment: 21 pages. v2: typos fixed, refs. added. v3: misprints corrected,
refs. adde
One-loop spectroscopy of semiclassically quantized strings: bosonic sector
We make a further step in the analytically exact quantization of spinning string states in semiclassical approximation, by evaluating the exact one-loop partition function for a class of two-spin string solutions for which quadratic fluctuations form a non-trivial system of coupled modes. This is the case of a folded string in the SU(2) sector, in the limit described by a quantum Landau–Lifshitz model. The same applies to the full bosonic sector of fluctuations over the folded spinning string in AdS5 with an angular momentum J in S5. Fluctuations are governed by a special class of fourth-order differential operators, with coefficients being meromorphic functions on the torus, which we are able to solve exactly
Finite-size corrections in the SU(2) x SU(2) sector of type IIA string theory on AdS_4 x CP^3
We consider finite-size corrections in the SU(2) x SU(2) sector of type IIA
string theory on AdS_4 x CP^3, which is the string dual of the recently
constructed N=6 superconformal Chern-Simons theory of Aharony, Bergman,
Jafferis and Maldacena (ABJM theory). The string states we consider are in the
R x S^2 x S^2 subspace of AdS_4 x CP^3 with an angular momentum J on CP^3 being
large. We compute the finite-size corrections using two different methods, one
is to consider curvature corrections to the Penrose limit giving an expansion
in 1/J, the other by considering a low energy expansion in lambda'=lambda/J^2
of the string theory sigma-model, lambda being the 't Hooft coupling of the
dual ABJM theory. For both methods there are interesting issues to deal with.
In the near-pp-wave method there is a 1/\sqrt{J} interaction term for which we
use zeta-function regularization in order to compute the 1/J correction to the
energy. For the low energy sigma-model expansion we have to take into account a
non-trivial coupling to a non-dynamical transverse direction. We find agreement
between the two methods. At order lambda' and lambda'^2, for small lambda', our
results are analogous to the ones for the SU(2) sector in type IIB string
theory on AdS_5 x S^5. Instead at order lambda'^3 there are interactions
between the two two-spheres. We compare our results with the recently proposed
all-loop Bethe ansatz of Gromov and Vieira and find agreement.Comment: 21 pages. v2: typos fixed, refs. added. v3: misprints corrected,
refs. adde
Two-dimensional S-matrices from unitarity cuts
Using unitarity methods, we compute, for several massive two-dimensional models, the cut-constructible part of the one-loop 2 → 2 scattering S-matrices from the tree-level amplitudes. We apply our method to various integrable theories, finding evidence that for supersymmetric models the one-loop S-matrix is cut-constructible, while for models without supersymmetry (but with integrability) the missing rational terms are proportional to the tree-level S-matrix and therefore can be interpreted as a shift in the coupling. Finally, applying our procedure to the world-sheet theory for the light-cone gauge-fixed AdS5 × S 5 superstring we reproduce, at one-loop in the near-BMN expansion, the S-matrix known from integrability techniques
Hidden Conformal Symmetry in Higher Derivative Dynamics for the Kerr Black Hole
The Kerr/CFT correspondence provides a holographic description of spinning black holes that exist in our universe and the notion of hidden conformal symmetry allows for a formulation of this correspondence that is away from extremality. In this study, we examined how hidden conformal symmetry is manifest when we consider dynamics beyond the Klein–Gordon equation through studying the analytic structure of the higher derivative equations of the motion of a massless probe scalar field on a Kerr background, using the monodromy method. Since such higher derivative dynamics appear in known examples of holographic AdS/logCFT correspondences, we investigated whether or not a Kerr/logCFT correspondence could be possible