66 research outputs found
Simple variables for AdS superspace
We introduce simple variables for describing the AdS
superspace, i. e. . The idea is to
embed the coset superspace into a space described by variables which are in
linear (ray) representations of the supergroup by imposing certain
supersymmetric quadratic constraints (up to two overall U(1) factors). The
construction can be considered as a supersymmetric generalisation of the
elementary realisations of the and the spaces by the SO(4,2) and
SO(6) invariant quadratic constraints on two six-dimensional flat spaces.Comment: 8 pages;v2 corrected typographical errors above the formula (5);v3
added comments at the end;v4 corrected typographical error
On membrane interactions and a three-dimensional analog of Riemann surfaces
Membranes in M-theory are expected to interact via splitting and joining
processes. We study these effects in the pp-wave matrix model, in which they
are associated with transitions between states in sectors built on vacua with
different numbers of membranes. Transition amplitudes between such states
receive contributions from BPS instanton configurations interpolating between
the different vacua. Various properties of the moduli space of BPS instantons
are known, but there are very few known examples of explicit solutions. We
present a new approach to the construction of instanton solutions interpolating
between states containing arbitrary numbers of membranes, based on a continuum
approximation valid for matrices of large size. The proposed scheme uses
functions on a two-dimensional space to approximate matrices and it relies on
the same ideas behind the matrix regularisation of membrane degrees of freedom
in M-theory. We show that the BPS instanton equations have a continuum
counterpart which can be mapped to the three-dimensional Laplace equation
through a sequence of changes of variables. A description of configurations
corresponding to membrane splitting/joining processes can be given in terms of
solutions to the Laplace equation in a three-dimensional analog of a Riemann
surface, consisting of multiple copies of R^3 connected via a generalisation of
branch cuts. We discuss various general features of our proposal and we also
present explicit analytic solutions.Comment: 64 pages, 17 figures. V2: An appendix, a figure and references added;
various minor changes and improvement
Membranes from monopole operators in ABJM theory: large angular momentum and M-theoretic AdS_4/CFT_3
We consider states with large angular momentum to facilitate the study of the
M-theory regime of the AdS_4/CFT_3 correspondence. We study the duality between
M-theory in AdS_4xS^7/Z_k and the ABJM N=6 Chern-Simons-matter theory with
gauge group U(N)xU(N) and level k, taking N large and k of order 1. In this
regime the lack of an explicit formulation of M-theory in AdS_4xS^7/Z_k makes
the gravity side difficult, while the CFT is strongly coupled and the planar
approximation is not applicable. To overcome these difficulties, we focus on
states on the gravity side with large angular momentum J>>1 and identify the
dual operators in the CFT, thereby establishing the AdS/CFT dictionary in this
sector. Natural approximation schemes arise on both sides thanks to the
presence of the small parameter 1/J. On the AdS side, we use the matrix model
of M-theory on the maximally supersymmetric pp-wave background with matrices of
size J/k. A perturbative treatment of this matrix model provides a good
approximation to M-theory in AdS_4xS^7/Z_k when N^{1/3}<<J<<N^{1/2}. On the CFT
side, we study the theory on S^2xR with magnetic flux J/k. A Born-Oppenheimer
type expansion arises naturally for large J in spite of the theory being
strongly coupled. The energy spectra on the two sides agree at leading order.
This provides a non-trivial test of the AdS_4/CFT_3 correspondence including
near-BPS observables associated with membrane degrees of freedom, thus
verifying the duality beyond the previously studied sectors corresponding to
either BPS observables or the type IIA string regime.Comment: 67 pages, 5 figures; V2: minor changes, references adde
On the continuity of the commutative limit of the 4d N=4 non-commutative super Yang-Mills theory
We study the commutative limit of the non-commutative maximally
supersymmetric Yang-Mills theory in four dimensions (N=4 SYM). The commutative
limits of non-commutative spaces are important in particular in the
applications of non-commutative spaces for regularisation of supersymmetric
theories (such as the use of non-commutative spaces as alternatives to lattices
for supersymmetric gauge theories and interpretations of some matrix models as
regularised supermembrane or superstring theories), which in turn can play a
prominent role in the study of quantum gravity via the gauge/gravity duality.
In general, the commutative limits are known to be singular and non-smooth due
to UV/IR mixing effects. We give a direct proof that UV effects do not break
the continuity of the commutative limit of the non-commutative N=4 SYM to all
order in perturbation theory, including non-planar contributions. This is
achieved by establishing the uniform convergence (with respect to the
non-commutative parameter) of momentum integrals associated with all Feynman
diagrams appearing in the theory, using the same tools involved in the proof of
finiteness of the commutative N=4 SYM.Comment: v1: 27 pages, 3 figures. v2: References update
Color Confinement and Bose-Einstein Condensation
We propose a unified description of two important phenomena: color
confinement in large- gauge theory, and Bose-Einstein condensation (BEC). We
focus on the confinement/deconfinement transition characterized by the increase
of the entropy from to , which persists in the weak coupling region.
Indistinguishability associated with the symmetry group -- SU() or O() in
gauge theory, and S permutations in the system of identical bosons -- is
crucial for the formation of the condensed (confined) phase. We relate standard
criteria, based on off-diagonal long range order (ODLRO) for BEC and the
Polyakov loop for gauge theory. The constant offset of the distribution of the
phases of the Polyakov loop corresponds to ODLRO, and gives the order parameter
for the partially-(de)confined phase at finite coupling. We demonstrate this
explicitly for several quantum mechanical systems (i.e., theories at small or
zero spatial volume) at weak coupling, and argue that this mechanism extends to
large volume and/or strong coupling. This viewpoint may have implications for
confinement at finite , and for quantum gravity via gauge/gravity duality.Comment: MH would like to dedicate this paper to Keitaro Nagata, who loved QCD
more than anybody else does. v2: The presentation was improved. The logic and
conclusion are unchanged. v3: References were added, some discussions were
elaborated, typographical errors in Appenx A were fixed. v4: Matches the
version accepted for publication in JHE
Universality in chaos: Lyapunov spectrum and random matrix theory
We propose the existence of a new universality in classical chaotic systems when the number of degrees of freedom is large: the statistical property of the Lyapunov spectrum is described by random matrix theory. We demonstrate it by studying the finite-time Lyapunov exponents of the matrix model of a stringy black hole and the mass-deformed models. The massless limit, which has a dual string theory interpretation, is special in that the universal behavior can be seen already at t=0, while in other cases it sets in at late time. The same pattern is demonstrated also in the product of random matrices
Holography at string field theory level: Conformal three point functions of BMN operators
A general framework for applying the pp-wave approximation to holographic
calculations in the AdS/CFT correspondence is proposed. By assuming the
existence and some properties of string field theory (SFT) on background, we extend the holographic ansatz proposed by Gubser, Klebanov,
Polyakov and Witten to SFT level. We extract relevant information of assumed
SFT on from its approximation, pp-wave SFT. As an explicit
example, we perform string theoretic calculations of the conformal three point
functions of the BMN operators. The results agree with the previous
calculations in gauge theory. We identify a broad class of field redefinitions,
including known ambiguities of the interaction Hamiltonian, which does not
affect the results.Comment: 1+12 page
Children with unilateral aural atresia
The effects of FM system fitted into the normal hearing ear (NHE) or a cartilage conduction hearing aid (CCHA) fitted into the affected ear (AE) on the speech recognition ability in noise were examined in children with unilateral congenital aural atresia (UCAA). In children with bilateral normal hearing (BNH), speech recognition score (SRS) was significantly decreased in the noisy environment of -5 dB signal-to-noise ratio (SNR), compared with those in quiet. In children with UCAA, SRS was significantly decreased in noisy environments of 0 and -5 dB SNR, compared with those in quiet. In noisy environments of 0 and -5 dB SNR, SRS in children with UCAA was significantly decreased, compared those in children with BNH. In the noisy environment of -5 dB SNR, SRS in UCAA children aided by FM system fitted into NHE was significantly better than those in unaided children in the same group. In the noisy environment of 0 dB SNR, SRS in UCAA children aided by CCHA into AE tended to be higher than those in unaided children in the same group. FM system and CCHA can be recommended as an audiological management for the improvement of speech recognition in children with UCHL in classrooms
Fuzzy Riemann Surfaces
We introduce C-Algebras (quantum analogues of compact Riemann surfaces),
defined by polynomial relations in non-commutative variables and containing a
real parameter that, when taken to zero, provides a classical non-linear,
Poisson-bracket, obtainable from a single polynomial C(onstraint) function. For
a continuous class of quartic constraints, we explicitly work out finite
dimensional representations of the corresponding C-Algebras
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