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- Hagedorn transition and chronology protection in string theoryPublication . Costa, Miguel S.; Herdeiro, Carlos A.R.; Penedones, J.; Sousa, NunoWe conjecture chronology is protected in string theory due to the condensation of light winding strings near closed null curves. This condensation triggers a Hagedorn phase transition, whose end-point target space geometry should be chronological. Contrary to conventional arguments, chronology is protected by an infrared effect. We support this conjecture by studying strings in the O-plane orbifold, where we show that some winding string states are unstable and condense in the non-causal region of spacetime. The oneloop string partition function has infrared divergences associated to the condensation of these states.
- Open descendants of U(2N) orbifolds at rational radiiPublication . Schellekens, Adrianus; Sousa, NunoWe construct explicitly the open descendants of some exceptional automorphism invariants of U(2N) orbifolds. We focus on the case N = p1×p2, p1 and P2 prime, and on the automorphisms of the diagonal and charge conjugation invariants that exist for these values of N. These correspond to orbifolds of the circle with radius R^2 = 2p1/p2. For each automorphism invariant we find two consistent Klein bottles, and for each Klein bottle we find a complete (and probably unique) set of boundary states. The two Klein bottles are in each case related to each other by simple currents, but surprisingly for the automorphism of the charge conjugation invariant neither of the Klein bottle choices is the canonical (symmetric) one.
- Klein bottles and simple currentsPublication . Huiszoon, Lennaert; Schellekens, Adrianus; Sousa, NunoThe standard Klein bottle coefficient in the construction of open descendants is shown to equal the Frobenius-Schur indicator of a conformal field theory. Other consistent Klein bottle projections are shown to correspond to simple currents. These observations enable us to generalize the standard open string construction from C-diagonal parent theories to include non-standard Klein bottles. Using (generalizations of) the Frobenius-Schur indicator we prove positivity and integrality of the resulting open and closed string state multiplicities for standard as well as non-standard Klein bottles.
- Orientation matters for NIMrepsPublication . Sousa, Nuno; Schellekens, AdrianusThe problem of finding boundary states in CFT, often rephrased in terms of “NIMreps” of the fusion algebra, has a natural extension to CFT on non-orientable surfaces. This provides extra information that turns out to be quite useful to give the proper interpretation to a NIMrep. We illustrate this with several examples. This includes a rather detailed discussion of the interesting case of the simple current extension of A2 level 9, which is already known to have a rich structure. This structure can be disentangled completely using orientation information. In particular we find here and in other cases examples of diagonal modular invariants that do not admit a NIMrep, suggesting that there does not exist a corresponding CFT. We obtain the complete set of NIMreps (plus Moebius and Klein bottle coefficients) for many exceptional modular invariants of WZW models, and find an explanation for the occurrence of more than one NIMrep in certain cases. We also (re)consider the underlying formalism, emphasizing the distinction between oriented and unoriented string annulus amplitudes, and the origin of orientation-dependent degeneracy matrices in the latter.
- Open descendants at c = 1Publication . Sousa, Nuno; Schellekens, BertA teoria de campo conforme do bosão livre na folha-universo de uma corda é estudada exaustivamente. São apresentados coeficientes de fronteira e cross-cap para bosões livres em orbivariedades de raio inteiro e racional. As condições de consistência pentagonais e hexagonais das matrizes de fusão e entrançamento são verificadas para alguns dos setores da teoria.
- Open descendants of non-diagonal invariantsPublication . Huiszoon, Lennaert; Schellekens, Adrianus; Sousa, NunoThe open descendants of simple current automorphism invariants are constructed. We consider the case where the order of the current is two or odd. We prove that our solutions satisfy the completeness conditions, positivity and integrality of the open and closed sectors and the Klein bottle constraint (apart from an interesting exception). In order to do this, we derive some new relations between the tensor Y and the fixed point conformal field theory. Some non-standard Klein bottle projections are considered as well.