No Arabic abstract
We construct various boundary states in the coset conformal field theory G/H. The G/H theory admits the twisted boundary condition if the G theory has an outer automorphism of the horizontal subalgebra that induces an automorphism of the H theory. By introducing the notion of the brane identification and the brane selection rule, we show that the twisted boundary states of the G/H theory can be constructed from those of the G and the H theories. We apply our construction to the su(n) diagonal cosets and the su(2)/u(1) parafermion theory to obtain the twisted boundary states of these theories.
We propose using smeared boundary states $e^{-tau H}|cal Brangle$ as variational approximations to the ground state of a conformal field theory deformed by relevant bulk operators. This is motivated by recent studies of quantum quenches in CFTs and of the entanglement spectrum in massive theories. It gives a simple criterion for choosing which boundary state should correspond to which combination of bulk operators, and leads to a rudimentary phase diagram of the theory in the vicinity of the RG fixed point corresponding to the CFT, as well as rigorous upper bounds on the universal amplitude of the free energy. In the case of the 2d minimal models explicit formulae are available. As a side result we show that the matrix elements of bulk operators between smeared Ishibashi states are simply given by the fusion rules of the CFT.
The g-function was introduced by Affleck and Ludwig as a measure of the ground state degeneracy of a conformal boundary condition. We consider this function for perturbations of the conformal Yang-Lee model by bulk and boundary fields using conformal perturbation theory, the truncated conformal space approach and the thermodynamic Bethe Ansatz (TBA). We find that the TBA equations derived by LeClair et al describe the massless boundary flows, up to an overall constant, but are incorrect when one considers a simultaneous bulk perturbation; however the TBA equations do correctly give the `non-universal linear term in the massive case, and the ratio of g-functions for different boundary conditions is also correctly produced. This ratio is related to the Y-system of the Yang-Lee model and by comparing the perturbative expansions of the Y-system and of the g-functions we obtain the exact relation between the UV and IR parameters of the massless perturbed boundary model.
The classification of rational conformal field theories is reconsidered from the standpoint of boundary conditions. Solving Cardys equation expressing the consistency condition on a cylinder is equivalent to finding integer valued representations of the fusion algebra. A complete solution not only yields the admissible boundary conditions but also gives valuable information on the bulk properties.
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.
Various observables in compact CFTs are required to obey positivity, discreteness, and integrality. Positivity forms the crux of the conformal bootstrap, but understanding of the abstract implications of discreteness and integrality for the space of CFTs is lacking. We systematically study these constraints in two-dimensional, non-holomorphic CFTs, making use of two main mathematical results. First, we prove a theorem constraining the behavior near the cusp of integral, vector-valued modular functions. Second, we explicitly construct non-factorizable, non-holomorphic cuspidal functions satisfying discreteness and integrality, and prove the non-existence of such functions once positivity is added. Application of these results yields several bootstrap-type bounds on OPE data of both rational and irrational CFTs, including some powerful bounds for theories with conformal manifolds, as well as insights into questions of spectral determinacy. We prove that in rational CFT, the spectrum of operator twists $tgeq {c over 12}$ is uniquely determined by its complement. Likewise, we argue that in generic CFTs, the spectrum of operator dimensions $Delta > {c-1over 12}$ is uniquely determined by its complement, absent fine-tuning in a sense we articulate. Finally, we discuss implications for black hole physics and the (non-)uniqueness of a possible ensemble interpretation of AdS$_3$ gravity.