232 research outputs found

### Strings and branes in plane waves

An overview of string theory in the maximally supersymmetric plane-wave
background is given, and some supersymmetric D-branes are discussed.Comment: 12 pages, LateX, needs fortschritte.sty; to appear in the proceedings
of the 36th International Symposium Ahrenshoop on the Theory of Elementary
Particles: Recent Developments in String/M-Theory and Field Theory, Berlin,
Germany, 26-30 Aug 200

### Fusion of twisted representations

The comultiplication formula for fusion products of untwisted representations
of the chiral algebra is generalised to include arbitrary twisted
representations. We show that the formulae define a tensor product with
suitable properties, and determine the analogue of Zhu's algebra for arbitrary
twisted representations.
As an example we study the fusion of representations of the Ramond sector of
the N=1 and N=2 superconformal algebra. In the latter case, certain subtleties
arise which we describe in detail.Comment: 24 pages, LATE

### Higher genus partition functions of meromorphic conformal field theories

It is shown that the higher genus vacuum amplitudes of a meromorphic
conformal field theory determine the affine symmetry of the theory uniquely,
and we give arguments that suggest that also the representation content with
respect to this affine symmetry is specified, up to automorphisms of the finite
Lie algebra. We illustrate our findings with the self-dual theories at c=16 and
c=24; in particular, we give an elementary argument that shows that the vacuum
amplitudes of the E_8\times E_8 theory and the Spin(32)/Z_2 theory differ at
genus g=5. The fact that the discrepancy only arises at rather high genus is a
consequence of the modular properties of higher genus amplitudes at small
central charges. In fact, we show that for c\leq 24 the genus one partition
function specifies already the partition functions up to g\leq 4 uniquely.
Finally we explain how our results generalise to non-meromorphic conformal
field theories.Comment: 43 pages, 7 figure

### The Continuous Orbifold of N=2 Minimal Model Holography

For the N=2 Kazama-Suzuki models that appear in the duality with a higher
spin theory on AdS_3 it is shown that the large level limit can be interpreted
as a continuous orbifold of 2N free bosons and fermions by the group U(N). In
particular, we show that the subset of coset representations that correspond to
the perturbative higher spin degrees of freedom are precisely described by the
untwisted sector of this U(N) orbifold. We furthermore identify the twisted
sector ground states of the orbifold with specific coset representations, and
give various pieces of evidence in favour of this identification.Comment: 24 pages, v2: minor correction

### Axiomatic Conformal Field Theory

A new rigorous approach to conformal field theory is presented. The basic
objects are families of complex-valued amplitudes, which define a meromorphic
conformal field theory (or chiral algebra) and which lead naturally to the
definition of topological vector spaces, between which vertex operators act as
continuous operators. In fact, in order to develop the theory, M\"obius
invariance rather than full conformal invariance is required but it is shown
that every M\"obius theory can be extended to a conformal theory by the
construction of a Virasoro field.
In this approach, a representation of a conformal field theory is naturally
defined in terms of a family of amplitudes with appropriate analytic
properties. It is shown that these amplitudes can also be derived from a
suitable collection of states in the meromorphic theory. Zhu's algebra then
appears naturally as the algebra of conditions which states defining highest
weight representations must satisfy. The relationship of the representations of
Zhu's algebra to the classification of highest weight representations is
explained.Comment: 51 pages, plain TE

### Higher Spins & Strings

It is natural to believe that the free symmetric product orbifold CFT is dual
to the tensionless limit of string theory on AdS3 x S3 x T4. At this point in
moduli space, string theory is expected to contain a Vasiliev higher spin
theory as a subsector. We confirm this picture explicitly by showing that the
large level limit of the N=4 cosets of arXiv:1305.4181, that are dual to a
higher spin theory on AdS3, indeed describe a closed subsector of the symmetric
product orbifold. Furthermore, we reorganise the full partition function of the
symmetric product orbifold in terms of representations of the higher spin
algebra (or rather its $W_{\infty}$ extension). In particular, the unbroken
stringy symmetries of the tensionless limit are captured by a large chiral
algebra which we can describe explicitly in terms of an infinite sum of
$W_{\infty}$ representations, thereby exhibiting a vast extension of the
conventional higher spin symmetry.Comment: 47 pages; ancillary file included; v2. typos corrected, minor changes
in Sec.

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