A Snapshot of J. L. Synge

A brief description is given of the life and influence on relativity theory of Professor J. L. Synge accompanied by some technical examples to illustrate his style of work

Hidden Yangian symmetry in sigma model on squashed sphere

We discuss a hidden symmetry of a two-dimensional sigma model on a squashed S^3. The SU(2) current can be improved so that it can be regarded as a flat connection. Then we can obtain an infinite number of conserved non-local charges and show the Yangian algebra by directly checking the Serre relation. This symmetry is also deduced from the coset structure of the squashed sphere. The same argument is applicable to the warped AdS_3 spaces via double Wick rotations.Comment: 11 pages, 1 figure, typos corrected, references adde

Comments on Non-holomorphic Modular Forms and Non-compact Superconformal Field Theories

We extend our previous work arXiv:1012.5721 [hep-th] on the non-compact N=2 SCFT_2 defined as the supersymmetric SL(2,R)/U(1)-gauged WZW model. Starting from path-integral calculations of torus partition functions of both the axial-type (`cigar') and the vector-type (`trumpet') models, we study general models of the Z_M-orbifolds and M-fold covers with an arbitrary integer M. We then extract contributions of the degenerate representations (`discrete characters') in such a way that good modular properties are preserved. The `modular completion' of the extended discrete characters introduced in arXiv:1012.5721 [hep-th] are found to play a central role as suitable building blocks in every model of orbifolds or covering spaces. We further examine a large M-limit (the `continuum limit'), which `deconstructs' the spectral flow orbits while keeping a suitable modular behavior. The discrete part of partition function as well as the elliptic genus is then expanded by the modular completions of irreducible discrete characters, which are parameterized by both continuous and discrete quantum numbers modular transformed in a mixed way. This limit is naturally identified with the universal cover of trumpet model. We finally discuss a classification of general modular invariants based on the modular completions of irreducible characters constructed above.Comment: 1+40 pages, no figure; v2 some points are clarified with respect to the `continuum limit', typos corrected, to appear in JHEP; v3 footnotes added in pages 18, 23 for the relation with arXiv:1407.7721[hep-th

The Spectrum of Strings on Warped AdS_3 x S^3

String theory on NS-NS AdS_3 x S^3 admits an exactly marginal deformation which breaks the SL(2,R)_R x SL(2,R)_L isometry of AdS_3 down to SL(2,R)_R x U(1)_L. The holographic dual is an exotic and only partially understood type of two-dimensional CFT with a reduced unbroken global conformal symmetry group. In this paper we study the deformed theory on the string worldsheet. It is found to be related by a spectral flow which is nonlocal in spacetime to the undeformed worldsheet theory. An exact formula for the spectrum of massive strings is presented.Comment: 26 pages, no figure

M-Horizons

We solve the Killing spinor equations and determine the near horizon geometries of M-theory that preserve at least one supersymmetry. The M-horizon spatial sections are 9-dimensional manifolds with a Spin(7) structure restricted by geometric constraints which we give explicitly. We also provide an alternative characterization of the solutions of the Killing spinor equation, utilizing the compactness of the horizon section and the field equations, by proving a Lichnerowicz type of theorem which implies that the zero modes of a Dirac operator coupled to 4-form fluxes are Killing spinors. We use this, and the maximum principle, to solve the field equations of the theory for some special cases and present some examples.Comment: 36 pages, latex. Reference added, minor typos correcte

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

Exact Results and Holography of Wilson Loops in N=2 Superconformal (Quiver) Gauge Theories

Using localization, matrix model and saddle-point techniques, we determine exact behavior of circular Wilson loop in N=2 superconformal (quiver) gauge theories. Focusing at planar and large `t Hooft couling limits, we compare its asymptotic behavior with well-known exponential growth of Wilson loop in N=4 super Yang-Mills theory. For theory with gauge group SU(N) coupled to 2N fundamental hypermultiplets, we find that Wilson loop exhibits non-exponential growth -- at most, it can grow a power of `t Hooft coupling. For theory with gauge group SU(N) x SU(N) and bifundamental hypermultiplets, there are two Wilson loops associated with two gauge groups. We find Wilson loop in untwisted sector grows exponentially large as in N=4 super Yang-Mills theory. We then find Wilson loop in twisted sector exhibits non-analytic behavior with respect to difference of two `t Hooft coupling constants. By letting one gauge coupling constant hierarchically larger/smaller than the other, we show that Wilson loops in the second type theory interpolate to Wilson loop in the first type theory. We infer implications of these findings from holographic dual description in terms of minimal surface of dual string worldsheet. We suggest intuitive interpretation that in both type theories holographic dual background must involve string scale geometry even at planar and large `t Hooft coupling limit and that new results found in the gauge theory side are attributable to worldsheet instantons and infinite resummation therein. Our interpretation also indicate that holographic dual of these gauge theories is provided by certain non-critical string theories.Comment: 52 pages, 7 figures v2. more figures embedded v3. minor stylistic changes, v4. published versio

String Theory on Warped AdS_3 and Virasoro Resonances

We investigate aspects of holographic duals to time-like warped AdS_3 space-times--which include G\"odel's universe--in string theory. Using worldsheet techniques similar to those that have been applied to AdS_3 backgrounds, we are able to identify space-time symmetry algebras that act on the dual boundary theory. In particular, we always find at least one Virasoro algebra with computable central charge. Interestingly, there exists a dense set of points in the moduli space of these models in which there is actually a second commuting Virasoro algebra, typically with different central charge than the first. We analyze the supersymmetry of the backgrounds, finding related enhancements, and comment on possible interpretations of these results. We also perform an asymptotic symmetry analysis at the level of supergravity, providing additional support for the worldsheet analysis.Comment: 24 pages + appendice

Sources of Financial Fragility: Financial Factors in the Economics of Capitalism

Originally, paper prepared for the conference, Coping with Financial Fragility: A Global Perspective, 7-9 September 1994, Maasdricht. (sic) Also included are handwritten and word processed pages showing original drafts of the paper

Financial Factors in the Economics of Capitalism

Journal of Financial Services Research, Vol 9, No. 3-4, 197-208