43 research outputs found
Analytic continuation of residue currents
Let be a complex manifold and f\colon X\to \C^p a holomorphic mapping
defining a complete intersection. We prove that the iterated Mellin transform
of the residue integral associated to has an analytic continuation to a
neighborhood of the origin in \C^p
Weighted integral formulas on manifolds
We present a method of finding weighted Koppelman formulas for -forms
on -dimensional complex manifolds which admit a vector bundle of rank
over , such that the diagonal of has a defining
section. We apply the method to \Pn and find weighted Koppelman formulas for
-forms with values in a line bundle over \Pn. As an application, we
look at the cohomology groups of -forms over \Pn with values in
various line bundles, and find explicit solutions to the \dbar-equation in
some of the trivial groups. We also look at cohomology groups of -forms
over \Pn \times \Pm with values in various line bundles. Finally, we apply
our method to developing weighted Koppelman formulas on Stein manifolds.Comment: 25 page
AdS/CFT correspondence in the Euclidean context
We study two possible prescriptions for AdS/CFT correspondence by means of
functional integrals. The considerations are non-perturbative and reveal
certain divergencies which turn out to be harmless, in the sense that
reflection-positivity and conformal invariance are not destroyed.Comment: 20 pages, references and two remarks adde
Classical and Quantum Strings in compactified pp-waves and Godel type Universes
We consider Neveu-Schwarz pp-waves with spacetime supersymmetry. Upon
compactification of a spacelike direction, these backgrounds develop Closed
Null Curves (CNCs) and Closed Timelike Curves (CTCs), and are U-dual to
supersymmetric Godel type universes. We study classical and quantum strings in
this background, with emphasis on the strings winding around the compact
direction. We consider two types of strings: long strings stabilized by NS flux
and rotating strings which are stabilized against collapse by angular momentum.
Some of the latter strings wrap around CNCs and CTCs, and are thus a potential
source of pathology. We analyze the partition function, and in particular
discuss the effects of these string states. Although our results are not
conclusive, the partition function seems to be dramatically altered due to the
presence of CNCs and CTCs. We discuss some interpretations of our results,
including a possible sign of unitary violation.Comment: 42 pages, LaTeX, 2 figure
Finite size corrections for open strings/open chains in planar AdS/CFT
We identify the leading finite-size (Luscher-type) correction to the energy
of open strings ending on maximal giant gravitons. In particular we obtain the
leading finite size correction at weak 't Hooft coupling and in the planar
limit to the energy of very short vacuum states. These results are shown to
agree with certain 1, 2, 3 and 4-loop dual gauge theory perturbative
calculations, which we also perform.Comment: 31 pages; v2: comments and references added; v3: clarifications and
references adde
The AdS(4) x CP(3) string and its Bethe equations in the near plane wave limit
We perform a detailed study of bosonic type IIA string theory in a large
light-cone momentum / near plane wave limit of . In order to
attain this we derive the Hamiltonian up to cubic and quartic order in number
of fields and calculate the energies for string excitations in a subspace. The computation for the string energies is performed for
arbitrary length excitations utilizing an unitary transformation which allows
us to remove the cubic terms in the Hamiltonian. We then rewrite a recent set
of proposed all loop Bethe equations in a light-cone language and compare their
predictions with the obtained string energies. We find perfect agreement.Comment: 28 pages, references and footnote adde
Giant Magnons in AdS4 x CP3: Embeddings, Charges and a Hamiltonian
This paper studies giant magnons in CP3, which in all known cases are old
solutions from S5 placed into two- and three-dimensional subspaces of CP3,
namely CP1, RP2 and RP3. We clarify some points about these subspaces, and
other potentially interesting three- and four-dimensional subspaces. After
confirming that E-(J1-J4)/2 is a Hamiltonian for small fluctuations of the
relevant 'vacuum' point particle solution, we use it to calculate the
dispersion relation of each of the inequivalent giant magnons. We comment on
the embedding of finite-J solutions, and use these to compare string solutions
to giant magnons in the algebraic curve.Comment: 17 pages (plus appendices) and 1 figure. v2 has new discussion of
placing finite-J giant magnons into CP^3, adds many references, and corrects
a few typo