94,922 research outputs found
Jain states on a torus: an unifying description
We analyze the modular properties of the effective CFT description for Jain
plateaux corresponding to the fillings nu=m/(2pm+1). We construct its
characters for the twisted and the untwisted sector and the diagonal partition
function. We show that the degrees of freedom entering the partition function
go to complete a Z_{m}-orbifold construction of the RCFT U(1)xSU(m)$ proposed
for the Jain states. The resulting extended algebra of the chiral primary
fields can be also viewed as a RCFT extension of the U(1)xW(m) minimal models.
For m=2 we prove that our model, the TM, gives the RCFT closure of the extended
minimal models U(1)xW(2).Comment: 27 pages, Latex, JHEP style, no figure
Limits of minimal models and continuous orbifolds
The lambda=0 't Hooft limit of the 2d W_N minimal models is shown to be
equivalent to the singlet sector of a free boson theory, thus paralleling
exactly the structure of the free theory in the Klebanov-Polyakov proposal. In
2d, the singlet sector does not describe a consistent theory by itself since
the corresponding partition function is not modular invariant. However, it can
be interpreted as the untwisted sector of a continuous orbifold, and this point
of view suggests that it can be made consistent by adding in the appropriate
twisted sectors. We show that these twisted sectors account for the `light
states' that were not included in the original 't Hooft limit. We also show
that, for the Virasoro minimal models (N=2), the twisted sector of our orbifold
agrees precisely with the limit theory of Runkel & Watts. In particular, this
implies that our construction satisfies crossing symmetry.Comment: 33 pages; v2: minor improvements and references added, published
versio
Feynman diagrams and minimal models for operadic algebras
We construct an explicit minimal model for an algebra over the cobar-construction of a differential graded operad. The structure maps of this minimal model are expressed in terms of sums over decorated trees. We introduce the appropriate notion of a homotopy equivalence of operadic algebras and show that our minimal model is homotopy equivalent to the original algebra. All this generalizes and gives a conceptual explanation of well-known results for A∞-algebras. Furthermore, we show that these results carry over to the case of algebras over modular operads; the sums over trees get replaced by sums over general Feynman graphs. As a by-product of our work we prove gauge-independence of Kontsevich's ‘dual construction’ producing graph cohomology classes from contractible differential graded Frobenius algebras
On the complete classification of the unitary N=2 minimal superconformal field theories
Aiming at a complete classification of unitary N=2 minimal models (where the
assumption of space-time supersymmetry has been dropped), it is shown that each
modular invariant candidate of a partition function for such a theory is indeed
the partition function of a minimal model. A family of models constructed via
orbifoldings of either the diagonal model or of the space-time supersymmetric
exceptional models demonstrates that there exists a unitary N=2 minimal model
for every one of the allowed partition functions in the list obtained from
Gannon's work.
Kreuzer and Schellekens' conjecture that all simple current invariants can be
obtained as orbifolds of the diagonal model, even when the extra assumption of
higher-genus modular invariance is dropped, is confirmed in the case of the
unitary N=2 minimal models by simple counting arguments.Comment: 53 pages; Latex; minor changes in v2: intro expanded, references
added, typos corrected, footnote added on p31; renumbering of sections; main
theorem reformulated for clarity, but contents unchanged. Minor revisions in
v3: typos corrected, footnotes 5, 6 added, lemma 1 and section 3.3.2
rewritten for greater generality, section 3.3 review removed. To appear in
Comm. Math. Phy
Rational Conformal Field Theories With G_2 Holonomy
We study conformal field theories for strings propagating on compact,
seven-dimensional manifolds with G_2 holonomy. In particular, we describe the
construction of rational examples of such models. We argue that analogues of
Gepner models are to be constructed based not on N=1 minimal models, but on Z_2
orbifolds of N=2 models. In Z_2 orbifolds of Gepner models times a circle, it
turns out that unless all levels are even, there are no new Ramond ground
states from twisted sectors. In examples such as the quintic Calabi-Yau, this
reflects the fact that the classical geometric orbifold singularity can not be
resolved without violating G_2 holonomy. We also comment on supersymmetric
boundary states in such theories, which correspond to D-branes wrapping
supersymmetric cycles in the geometry.Comment: 20 pages, harvmac(b); v2: ref. adde
The Gravity Dual of the Ising Model
We evaluate the partition function of three dimensional theories of gravity
in the quantum regime, where the AdS radius is Planck scale and the central
charge is of order one. The contribution from the AdS vacuum sector can - with
certain assumptions - be computed and equals the vacuum character of a minimal
model CFT. The torus partition function is given by a sum over geometries which
is finite and computable. For generic values of Newton's constant G and the AdS
radius L the result has no Hilbert space interpretation, but in certain cases
it agrees with the partition function of a known CFT. For example, the
partition function of pure Einstein gravity with G=3L equals that of the Ising
model, providing evidence that these theories are dual. We also present
somewhat weaker evidence that the 3-state and tricritical Potts models are dual
to pure higher spin theories of gravity based on SL(3) and E_6, respectively.Comment: 42 page
The Most Irrational Rational Theories
We propose a two-parameter family of modular invariant partition functions of
two-dimensional conformal field theories (CFTs) holographically dual to pure
three-dimensional gravity in anti de Sitter space. Our two parameters control
the central charge, and the representation of . At large
central charge, the partition function has a gap to the first nontrivial
primary state of . As the representation
dimension gets large, the partition function exhibits some of the qualitative
features of an irrational CFT. This, for instance, is captured in the behavior
of the spectral form factor. As part of these analyses, we find similar
behavior in the minimal model spectral form factor as approaches .Comment: 25 pages plus appendices, 11 figure
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