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We study aspects of anti-de Sitter space in the context of the Swampland. In particular, we conjecture that the near-flat limit of pure AdS belongs to the Swampland, as it is necessarily accompanied by an infinite tower of light states. The mass of the tower is power-law in the cosmological constant, with a power of $\frac{1}{2}$ for the supersymmetric case. We discuss relations between this behaviour and other Swampland conjectures such as the censorship of an unbounded number of massless fields, and the refined de Sitter conjecture. Moreover, we propose that changes to the AdS radius have an interpretation in terms of a generalised distance conjecture which associates a distance to variations of all fields. In this framework, we argue that the distance to the $\Lambda \rightarrow 0$ limit of AdS is infinite, leading to the light tower of states. We also discuss implications of the conjecture for de Sitter space., Comment: 8 pages. v2: fixed typos and added references

Recent work on F-theory GUTs has shown that the predicted masses, and magnitudes of the mixing matrix elements in the quark and lepton sectors are in close accord with experiment. In this note we estimate the CP violating phase of the mixing matrices by considering the Jarlskog invariant. We find by carefully treating certain cancellations in the computation of the Jarlskog invariant that |J_quark| ~ alpha_GUT^(3) ~ 6*10^(-5), and that the CP violating phase of the quark sector is large, in accord with experiment. Moreover, we predict (up to order one factors) that |J_lepton| ~ alpha_GUT ~ 4*10^(-2) and that the CP violating phase of the lepton sector is also large., Comment: v2: 3 pages, Improved estimate of the Jarlskog invariant involving subtle cancellations, leading to a different conclusion for the CP violating phase

We find integrable deformations of the N = 2 supersymmetric minimal series of conformal models by discovering supermultiplets of conserved currents in the perturbed theories. Integrability for these models is closely related to the geometric structure of the perturbed superpotentials. The exact soliton spectrum can be read off from the superpotential and this is then used to determine the purely elastic scattering matrices for the perturbed massive theories.

By modifying the definition of the fermion number projection in the E 8 × E 8 heterotic superstring theory in a manner consistent with modular invariance and factorization, a tachyon-free string theory is obtained without spacetime supersymmetry. The low energy limit is a ten-dimensional anomaly-free chiral SO(16) × SO(16) gauge theory coupled to gravity.

We define conformal theories as realizations of certain operations involving punctured Riemann surfaces (with coordinates chosen at the punctures) in a Hilbert space. We describe the connections of our formalism with other formulations of conformal theories.

By studying the representations of the mapping class groups which arise in 2D conformal theories we derive some restrictions on the value of the conformal dimension hi of operators and the central charge c of the Virasoro algebra. As a simple application we show that when there are a finite number of operators in the conformal algebra, the hi and c are all rational.

We use symmetries of the path-integral on Riemann surfaces with boundaries to develop an operator formulation for higher loop Riemann surfaces.

Using ideas from renormalization group theory we show that the study of catastrophes (singularities) is a powerful tool in the classification of conformal theories. The results are most powerful when applied to N =2 superconformal models. The ideas are illustrated by considering some examples including the minimal superconformal models.

The equivalence is proved between fermionic and scalar field theories on Riemann surfaces of arbitrary topology. The effects of global topology include a modification of the bosonic action.

In this note we briefly discuss some topological structures of the space of 2D QFTs. Our main tool is the consideration of Zamalodchikov's c function as a Morse function of this space.

We discuss some aspects of symmetry breakings in string theories. We mainly focus on the algebra of bosonic strings, but suspect similar ideas may be used for superstring theories. We point out a curious relation between the partition function of certain bosonic string theories and superstring theories.