1,721,028 research outputs found
Ising model and N=2 supersymmetric theories
No full textWe establish a direct link between massive Ising model and arbitrary massive N = 2 supersymmetric QFT's in two dimensions. This explains why the equations which appear in the computation of spin-correlations in the non-critical Ising model are the same as those describing the geometry of vacua in N = 2 theories. The tau-function appearing in the Ising model (i.e., the spin correlation function) is reinterpreted in the N = 2 context as a new ''index''. In special cases this new index is related to the Ray-Singer analytic torsion, and can be viewed as a generalization of that to the loop space of Kahler manifolds
Massive orbifolds
No full textWe study some aspects of 2D supersymmetric sigma models on orbifolds. It turns out that independently of whether the 2D QFT is conformal the operator products of twist operators are non-singular, suggesting that massive (non-conformal) orbifolds also "resolve singularities" just as in the conformal case. Moreover we recover the OPE of twist operators for conformal theories by considering the uv limit of the massive orbifold correlation functions. Alternatively, we can use the OPE of twist fields at the conformal point to derive conditions for the existence of non-singular solutions to special nonlinear differential equations (such as Painleve III)
Exact results for supersymmetric sigma models
No full textWe show that the metric and Berry's curvature for the ground states of N = 2 supersymmetric sigma-models can be computed exactly as one varies the Kahler structure. For the case of CP(n) these are related to special solutions of affine Toda equations. This allows us to extract exact results. We find that the ground-state metric is nonsingular as the size of the manifold shrinks to zero, suggesting that 2D quantum field theory makes sense even beyond zero radius. Thus it seems that manifolds with zero size are nonsingular as target spaces for string theory (even when they are not conformal)
Classification of complete N=2 supersymmetric theories in 4 dimensions
No full textWe define the notion of a complete N= 2 supersymmetric theory in 4 dimensions as one which has a maximal allowed dimension for a UV complete moduli space for the coupling constants, masses and Coulomb branch parameters. We classify all such theories whose BPS spectrum can be obtained via a quiver diagram. This is done using the 4d/2d correspondence and by showing that such complete N=2 theories map to quivers of finite mutation type. The list of such theories is given by the Gaiotto theories consisting of two 5-branes wrapping Riemann surfaces with punctures, as well as 11 additional exceptional cases, which we identify. Copyright © by International Press of Boston, Inc
Topological anti-topological fusion
No full textWe study some non-perturbative aspects of N = 2 supersymmetric quantum field theories (both superconformal and massive deformations thereof). We show that the metric for the supersymmetric ground states, which in the conformal limit is essentially the same as Zamolodchikov's metric, is pseudo-topological and can be viewed as a result of fusion of the topological version of N = 2 theory with its conjugate. For special marginal/relevant deformations (corresponding to theories with factorizable S-matrix), the ground state metric satisfies classical Toda/Affine Toda equations as a function of perturbation parameters. The unique consistent boundary conditions for these differential equations seem to predict the normalized OPE of chiral fields at the conformal point. Also the subset of N = 2 theories whose chiral ring is isomorphic to SU(N)k Verlinde ring turns out to lead to affine Toda equations of SU(N) type satisfied by the ground state metric
Twistorial topological strings and a tt* geometry for N =2 theories in 4d
No full textWe define twistorial topological strings by considering tt* geometry of the 4d N =2 supersymmetric theories on the Nekrasov- Shatashvili 1/2Ω background, which leads to quantization of the associated hyperKähler geometries. We show that in one limit it reduces to the refined topological string amplitude. In another limit it is a solution to a quantum Riemann-Hilbert problem involving quantum Kontsevich-Soibelman operators. In a further limit it encodes the hyperKähler integrable systems studied by GMN. In the context of AGT conjecture, this perspective leads to a twistorial extension of Toda. The 2d index of the 1/2Ω theory leads to the recently introduced index for N =2 theories in 4d. The twistorial topological string can alternatively be viewed, using the work of Nekrasov-Witten, as studying the vacuum geometry of 4d N =2 supersymmetric theories on T2 × I where I is an interval with specific boundary conditions at the two ends
Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes
No full textWe develop techniques to compute higher loop string amplitudes for twisted N = 2 theories with c = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a particular realization of the N = 2 theories, the resulting string field theory is equivalent to a topological theory in six dimensions, the Kodaira-Spencer theory, which may be viewed as the closed string analog of the Chern-Simons theory. Using the mirror map this leads to computation of the 'number' of holomorphic curves of higher genus curves in Calabi-Yau manifolds. It is shown that topological amplitudes can also be reinterpreted as computing corrections to superpotential terms appearing in the effective 4d theory resulting from compactification of standard 10d superstrings on the corresponding N = 2 theory. Relations with c = 1 strings are also pointed out
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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