No Arabic abstract
We extend the definition of the refined topological vertex C to an n-coloured refined topological vertex C_n that depends on n free bosons, and compute the 5D strip partition function made of N pairs of C_n vertices and conjugate C*_n vertices. Using geometric engineering and the AGT correspondence, the 4D limit of this strip partition function is identified with a (normalized) matrix element of a (primary state) vertex operator that intertwines two (arbitrary descendant) states in a (generically non-rational) 2D conformal field theory with Z_n parafermion primary states.
Supersymmetric theories with the same bosonic content but different fermions, aka emph{twins}, were thought to exist only for supergravity. Here we show that pairs of super conformal field theories, for example exotic $mathcal{N}=3$ and $mathcal{N}=1$ theories in $D=4$ spacetime dimensions, can also be twin. We provide evidence from three different perspectives: (i) a twin S-fold construction, (ii) a double-copy argument and (iii) by identifying candidate twin holographically dual gauged supergravity theories. Furthermore, twin W-supergravity theories then follow by applying the double-copy prescription to exotic super conformal field theories.
The loss of criticality in the form of weak first-order transitions or the end of the conformal window in gauge theories can be described as the merging of two fixed points that move to complex values of the couplings. When the complex fixed points are close to the real axis, the system typically exhibits walking behavior with Miransky (or Berezinsky-Kosterlitz-Thouless) scaling. We present a novel realization of these phenomena at strong coupling by means of the gauge/gravity duality, and give evidence for the conjectured existence of complex conformal field theories at the fixed points.
We consider Deep Inelastic Scattering (DIS) thought experiments in unitary Conformal Field Theories (CFTs). We explore the implications of the standard dispersion relations for the OPE data. We derive positivity constraints on the OPE coefficients of minimal-twist operators of even spin s geq 2. In the case of s=2, when the leading-twist operator is the stress tensor, we reproduce the Hofman-Maldacena bounds. For s>2 the bounds are new.
An account is given of the structure and representations of chiral bosonic meromorphic conformal field theories (CFTs), and, in particular, the conditions under which such a CFT may be extended by a representation to form a new theory. This general approach is illustrated by considering the untwisted and $Z_2$-twisted theories, $H(Lambda)$ and $tilde H(Lambda)$ respectively, which may be constructed from a suitable even Euclidean lattice $Lambda$. Similarly, one may construct lattices $Lambda_C$ and $tildeLambda_C$ by analogous constructions from a doubly-even binary code $C$. In the case when $C$ is self-dual, the corresponding lattices are also. Similarly, $H(Lambda)$ and $tilde H(Lambda)$ are self-dual if and only if $Lambda$ is. We show that $H(Lambda_C)$ has a natural ``triality structure, which induces an isomorphism $H(tildeLambda_C)equivtilde H(Lambda_C)$ and also a triality structure on $tilde H(tildeLambda_C)$. For $C$ the Golay code, $tildeLambda_C$ is the Leech lattice, and the triality on $tilde H(tildeLambda_C)$ is the symmetry which extends the natural action of (an extension of) Conways group on this theory to the Monster, so setting triality and Frenkel, Lepowsky and Meurmans construction of the natural Monster module in a more general context. The results also serve to shed some light on the classification of self-dual CFTs. We find that of the 48 theories $H(Lambda)$ and $tilde H(Lambda)$ with central charge 24 that there are 39 distinct ones, and further that all 9 coincidences are accounted for by the isomorphism detailed above, induced by the existence of a doubly-even self-dual binary code.
Following on from earlier work relating modules of meromorphic bosonic conformal field theories to states representing solutions of certain simple equations inside the theories, we show, in the context of orbifold theories, that the intertwiners between twisted sectors are unique and described explicitly in terms of the states corresponding to the relevant modules. No explicit knowledge of the structure of the twisted sectors is required. Further, we propose a general set of sufficiency conditions, illustrated in the context of a third order no-fixed-point twist of a lattice theory, for verifying consistency of arbitrary orbifold models in terms of the states representing the twisted sectors.