The non-compact elliptic genus: mock or modular

We analyze various perspectives on the elliptic genus of non-compact supersymmetric coset conformal field theories with central charge larger than three. We calculate the holomorphic part of the elliptic genus via a free field description of the model, and show that it agrees with algebraic expectations. The holomorphic part of the elliptic genus is directly related to an Appell-Lerch sum and behaves anomalously under modular transformation properties. We analyze the origin of the anomaly by calculating the elliptic genus through a path integral in a coset conformal field theory. The path integral codes both the holomorphic part of the elliptic genus, and a non-holomorphic remainder that finds its origin in the continuous spectrum of the non-compact model. The remainder term can be shown to agree with a function that mathematicians introduced to parameterize the difference between mock theta functions and Jacobi forms. The holomorphic part of the elliptic genus thus has a path integral completion which renders it non-holomorphic and modular.Comment: 13 page

Higher Loop Spin Field Correlators in D=4 Superstring Theory

We develop calculational tools to determine higher loop superstring correlators involving massless fermionic and spin fields in four space time dimensions. These correlation functions are basic ingredients for the calculation of loop amplitudes involving both bosons and fermions in D=4 heterotic and superstring theories. To obtain the full amplitudes in Lorentz covariant form the loop correlators of fermionic and spin fields have to be expressed in terms of SO(1,3) tensors. This is one of the main achievements in this work.Comment: 59 pages, 1 figure; v2: final version published in JHE

Yukawa hierarchies at the point of E8E_8 in F-theory

We analyse the structure of Yukawa couplings in local SU(5) F-theory models with $E_8$ enhancement. In this setting the $E_8$ symmetry is broken down to SU(5) by a 7-brane configuration described by T-branes, all the Yukawa couplings are generated in the vicinity of a point and only one family of quarks and leptons is massive at tree-level. The other two families obtain their masses when non-perturbative effects are taken into account, being hierarchically lighter than the third family. However, and contrary to previous results, we find that this hierarchy of fermion masses is not always appropriate to reproduce measured data. We find instead that different T-brane configurations breaking $E_8$ to SU(5) give rise to distinct hierarchical patterns for the holomorphic Yukawa couplings. Only some of these patterns allow to fit the observed fermion masses with reasonable local model parameter values, adding further constraints to the construction of F-theory GUTs. We consider an $E_8$ model where such appropriate hierarchy is realised and compute its physical Yukawas, showing that realistic charged fermions masses can indeed be obtained in this case.Comment: 46 pages + appendices, 5 figures. v2, added references and typos corrected, version accepted on JHEP. v3, typos correcte

Boundary conditions in Toda theories and minimal models

We show that the disc bulk one-point functions in a sl(n) Toda conformal field theory have a well-defined limit for the central charge c=n-1, and that their limiting values can be obtained from a limit of bulk one-point functions in the W_n minimal models. This comparison leads to a proposal for one-point functions for twisted boundary conditions in Toda theory.Comment: 33 pages, 1 figure; v2: Minor corrections; v3: version accepted at JHE

The relationship between the presence of anti-cyclic citrullinated peptide antibodies and clinical phenotype in very early rheumatoid arthritis

<p>Abstract</p> <p>Background</p> <p>Anti-cyclic citrullinated peptide (anti-CCP) antibodies are highly specific for RA, but are not detectable in all RA patients. The aim of this study was to establish whether the clinical phenotypes of anti-CCP positive and negative disease are distinct at the earliest clinically apparent phase of disease.</p> <p>Methods</p> <p>Patients were recruited from the Birmingham early inflammatory arthritis clinic. Participants were included in the current study if they presented within 3 months of symptom onset and fulfilled 1987 ACR criteria for RA at some point during an 18 month follow-up. Data were collected on demographic variables, joint symptoms and tender (n = 68) and swollen (n = 66) joint counts. CRP, ESR, rheumatoid factor and anti-CCP2 status were measured.</p> <p>Results</p> <p>92 patients were included (48 anti-CCP positive). The anti-CCP positive and negative groups were comparable in terms of demographic variables, inflammatory markers, joint counts and 1987 ACR classification criteria, except that more anti-CCP positive patients were rheumatoid factor positive (83.3% vs. 11.4%, p < 0.01). There was no significant difference in the pattern of joint involvement, except for an increased prevalence of knee joint swelling in anti-CCP positive patients (42.9% vs. 22.2%, p = 0.03).</p> <p>Conclusions</p> <p>Patients with and without anti-CCP antibodies present in a similar way, even within three months of clinically apparent disease that eventually develops into RA.</p

Dual Boundary Conditions in 3d SCFT's

We propose matching pairs of half-BPS boundary conditions related by IR dualities of 3d $\mathcal{N}=2$ gauge theories. From these matching pairs we construct duality interfaces. We test our proposals by anomaly matching and the computation of supersymmetric indices. Examples include basic abelian dualities, level-rank dualities, and Aharony dualities.Comment: 99 pages, 3 figures. v2: minor edits, appendix on Weyl-Kac formula adde

Supersymmetry: From the Fermi Scale to the Planck Scale

The physics of supersymmetry is reviewed from the perspective of physics at ever increasing energies. Starting from the minimal supersymmetric extension of the Standard Model at the electroweak scale, we proceed to higher energies seeking to understand the origin of the many model parameters. Supersymmetric grand unification, supergravity, and superstrings are introduced sequentially, and their contribution to the sought explanations is discussed. Typical low-energy supersymmetric models are also presented, along with their possible experimental consequences via direct and indirect processes at high-energy physics experimental facilities. Contents 1. Introduction 2. Low-energy Supersymmetry 3. Supersymmetric Grand Unification 4. Supergravity 5. Superstrings 6. Dynamics 7. Experimental Prospects 8. ConclusionsComment: 61 pages, LaTeX, 11 figures (included). To appear in Reports on Progress in Physic