40,267 research outputs found
Instantons, Twistors, and Emergent Gravity
Motivated by potential applications to holography on space-times of positive
curvature, and by the successful twistor description of scattering amplitudes,
we propose a new dual matrix formulation of N = 4 gauge theory on S(4). The
matrix model is defined by taking the low energy limit of a holomorphic
Chern-Simons theory on CP(3|4), in the presence of a large instanton flux. The
theory comes with a choice of S(4) radius L and a parameter N controlling the
overall size of the matrices. The flat space variant of the 4D effective theory
arises by taking the large N scaling limit of the matrix model, with l_pl^2 ~
L^2 / N held fixed. Its massless spectrum contains both spin one and spin two
excitations, which we identify with gluons and gravitons. As shown in the
companion paper, the matrix model correlation functions of both these
excitations correctly reproduce the corresponding MHV scattering amplitudes. We
present evidence that the scaling limit defines a gravitational theory with a
finite Planck length. In particular we find that in the l_pl -> 0 limit, the
matrix model makes contact with the CSW rules for amplitudes of pure gauge
theory, which are uncontaminated by conformal supergravity. We also propose a
UV completion for the system by embedding the matrix model in the physical
superstring.Comment: v2: 64 pages, 3 figures, references added, typos correcte
Supersymmetric theories on squashed five-sphere
We construct supersymmetric theories on the SU(3)xU(1) symmetric squashed
five-sphere with 2, 4, 6, and 12 supercharges. We first determine the Killing
equation by dimensional reduction from 6d, and use Noether procedure to
construct actions. The supersymmetric Yang-Mills action is straightforwardly
obtained from the supersymmetric Chern-Simons action by using a supersymmetry
preserving constant vector multiplet.Comment: 20 pages, no figure, LaTeX; v3: minor corrections, accepted for
publication in PTE
Quantum contact interactions
The existence of several exotic phenomena, such as duality and spectral
anholonomy is pointed out in one-dimensional quantum wire with a single defect.
The topological structure in the spectral space which is behind these phenomena
is identified.Comment: A lecture presented at the 2nd Winter Institute on Foundations of
Quantum Theory and Quantum Optics (WINST02), Jan. 2-11, 2002, S.N.Bose
Institute, Calcutta, India: 8 pages latex with Indian Acad. Sci. style fil
Higher spin matrix models
We propose a hybrid class of theories for higher spin gravity and matrix
models, i.e. which handle simultaneously higher spin gravity fields and matrix
models. The construction is similar to Vasiliev's higher spin gravity but part
of the equations of motion are provided by the action principle of a matrix
model. In particular we construct a higher spin (gravity) matrix model related
to type IIB matrix models/string theory which have a well defined classical
limit, and which is compatible with higher spin gravity in space. As it
has been suggested that higher spin gravity should be related to string theory
in a high energy (tensionless) regime, and therefore to M-Theory, we expect
that our construction will be useful to explore concrete connections.Comment: 13 pages, 1 table. New references and corrections from referee
reports are included in this version. Current form accepted in Universe
journal for the special issue on Higher Spin Gauge Theorie
The classical R-matrix of AdS/CFT and its Lie dialgebra structure
The classical integrable structure of Z_4-graded supercoset sigma-models,
arising in the AdS/CFT correspondence, is formulated within the R-matrix
approach. The central object in this construction is the standard R-matrix of
the Z_4-twisted loop algebra. However, in order to correctly describe the Lax
matrix within this formalism, the standard inner product on this twisted loop
algebra requires a further twist induced by the Zhukovsky map, which also plays
a key role in the AdS/CFT correspondence. The non-ultralocality of the
sigma-model can be understood as stemming from this latter twist since it leads
to a non skew-symmetric R-matrix.Comment: 22 pages, 2 figure
Supersymmetric backgrounds from 5d N=1 supergravity
We construct curved backgrounds with Euclidean signature admitting rigid
supersymmetry by using a 5d N=1 off-shell Poincare supergravity. We solve the
conditions for the background Weyl multiplet and vector multiplets that
preserve at least one supersymmetry parameterized by a symplectic Majorana
spinor, and represent the solution in terms of several independent fields. We
also show that the partition function does not depends on the local degrees of
freedom of the background fields. Namely, as far as we focus on a single
coordinate patch, we can freely change the independent fields by combining
Q-exact deformations and gauge transformations. We also discuss realization of
several known examples of supersymmetric theories in curved backgrounds by
using the supergravity.Comment: 31 pages, no figures; v2: references adde
Quantum Gravity on the Lattice
I review the lattice approach to quantum gravity, and how it relates to the
non-trivial ultraviolet fixed point scenario of the continuum theory. After a
brief introduction covering the general problem of ultraviolet divergences in
gravity and other non-renormalizable theories, I cover the general methods and
goals of the lattice approach. An underlying theme is the attempt at
establishing connections between the continuum renormalization group results,
which are mainly based on diagrammatic perturbation theory, and the recent
lattice results, which apply to the strong gravity regime and are inherently
non-perturbative. A second theme in this review is the ever-present natural
correspondence between infrared methods of strongly coupled non-abelian gauge
theories on the one hand, and the low energy approach to quantum gravity based
on the renormalization group and universality of critical behavior on the
other. Towards the end of the review I discuss possible observational
consequences of path integral quantum gravity, as derived from the non-trivial
ultraviolet fixed point scenario. I argue that the theoretical framework
naturally leads to considering a weakly scale-dependent Newton's costant, with
a scaling violation parameter related to the observed scaled cosmological
constant (and not, as naively expected, to the Planck length).Comment: 63 pages, 12 figure
Supersymmetric gauge theories on five-manifolds
We construct rigid supersymmetric gauge theories on Riemannian
five-manifolds. We follow a holographic approach, realizing the manifold as the
conformal boundary of a six-dimensional bulk supergravity solution. This leads
to a systematic classification of five-dimensional supersymmetric backgrounds
with gravity duals. We show that the background metric is furnished with a
conformal Killing vector, which generates a transversely holomorphic foliation
with a transverse Hermitian structure. Moreover, we prove that any such metric
defines a supersymmetric background. Finally, we construct supersymmetric
Lagrangians for gauge theories coupled to arbitrary matter on such backgrounds.Comment: 35 pages: v2: minor corrections and references added. Published
versio
Heterotic M-theory in Five Dimensions
We derive the five-dimensional effective action of strongly coupled heterotic
string theory for the complete (1,1) sector of the theory by performing a
reduction, on a Calabi-Yau three-fold, of M-theory on S^1/Z_2. A crucial
ingredient for a consistent truncation is a non-zero mode of the antisymmetric
tensor field strength which arises due to magnetic sources on the orbifold
planes. The correct effective theory is a gauged version of five-dimensional
N=1 supergravity coupled to Abelian vector multiplets, the universal
hypermultiplet and four-dimensional boundary theories with gauge and gauge
matter fields. The gauging is such that the dual of the four-form field
strength in the universal multiplet is charged under a particular linear
combination of the Abelian vector fields. In addition, the theory has potential
terms for the moduli in the bulk as well as on the boundary. Because of these
potential terms, the supersymmetric ground state of the theory is a
multi-charged BPS three-brane domain wall, which we construct in general. We
show that the five-dimensional theory together with this solution provides the
correct starting point for particle phenomenology as well as early universe
cosmology. As an application, we compute the four-dimensional N=1 supergravity
theory for the complete (1,1) sector to leading nontrivial order by a reduction
on the domain wall background. We find a correction to the matter field Kahler
potential and threshold corrections to the gauge kinetic functions.Comment: 47 pages, Latex 2e with amsmath, typos removed, some factors
correcte
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