Relating prepotentials and quantum vacua of N=1 gauge theories with different tree-level superpotentials

We consider N=1 supersymmetric U(N) gauge theories with Z_k symmetric tree-level superpotentials W for an adjoint chiral multiplet. We show that (for integer 2N/k) this Z_k symmetry survives in the quantum effective theory as a corresponding symmetry of the effective superpotential W_eff(S_i) under permutations of the S_i. For W(x)=^W(h(x)) with h(x)=x^k, this allows us to express the prepotential F_0 and effective superpotential W_eff on certain submanifolds of the moduli space in terms of an ^F_0 and ^W_eff of a different theory with tree-level superpotential ^W. In particular, if the Z_k symmetric polynomial W(x) is of degree 2k, then ^W is gaussian and we obtain very explicit formulae for F_0 and W_eff. Moreover, in this case, every vacuum of the effective Veneziano-Yankielowicz superpotential ^W_eff is shown to give rise to a vacuum of W_eff. Somewhat surprisingly, at the level of the prepotential F_0(S_i) the permutation symmetry only holds for k=2, while it is anomalous for k>2 due to subtleties related to the non-compact period integrals. Some of these results are also extended to general polynomial relations h(x) between the tree-level superpotentials.Comment: 27 pages, 10 figures, modified version to appear in JHEP, discussion of the physical meaning of the Z_k symmetry adde

Multi-Component KdV Hierarchy, V-Algebra and Non-Abelian Toda Theory

I prove the recently conjectured relation between the $2\times 2$-matrix differential operator $L=\partial^2-U$, and a certain non-linear and non-local Poisson bracket algebra ($V$-algebra), containing a Virasoro subalgebra, which appeared in the study of a non-abelian Toda field theory. Here, I show that this $V$-algebra is precisely given by the second Gelfand-Dikii bracket associated with $L$. The Miura transformation is given which relates the second to the first Gelfand-Dikii bracket. The two Gelfand-Dikii brackets are also obtained from the associated (integro-) differential equation satisfied by fermion bilinears. The asymptotic expansion of the resolvent of $(L-\xi)\Psi=0$ is studied and its coefficients $R_l$ yield an infinite sequence of hamiltonians with mutually vanishing Poisson brackets. I recall how this leads to a matrix KdV hierarchy which are flow equations for the three component fields $T, V^+, V^-$ of $U$. For $V^\pm=0$ they reduce to the ordinary KdV hierarchy. The corresponding matrix mKdV equations are also given, as well as the relation to the pseudo- differential operator approach. Most of the results continue to hold if $U$ is a hermitian $n\times n$-matrix. Conjectures are made about $n\times n$-matrix $m^{\rm th}$-order differential operators $L$ and associated $V_{(n,m)}$-algebras.Comment: 20 pages, revised: several references to earlier papers on multi-component KdV equations are adde

A Review of Hearing Loss in Cleft Palate Patients

Background. Cleft palate is associated with recurrent otitis media with effusion and hearing loss. This study analysed the way these patients' hearing is managed in Alder Hey Children's Hospital. Method. A retrospective audit was carried out on cleft palate patients in Alder Hey Children's Hospital. Audiology assessment and treatment options were reviewed. Comparisons were made between the use of ventilation tubes (VTs) and hearing aids (HAs). The types of cleft, types of hearing loss, and the management output of the audiology regions were also reviewed. Results. The audiology assessments of 254 patients were examined. The incidence of VT insertion in this group of patients was 18.9%. The hearing aid incidence rate was 10.1%. The VT-related complication rate was 25.5% and the HA related complication rate was 9.1%. Conclusion. The data demonstrates that both treatments are viable, and a new protocol which combines the short term benefit of VT insertion with the lower complication rate of HA is required

Comments on Supersymmetric Vector and Matrix Models

Some results in random matrices are generalized to supermatrices, in particular supermatrix integration is reduced to an integration over the eigenvalues and the resulting volume element is shown to be equivalent to a one dimensional Coulomb gas of both positive and negative charges.It is shown that,for polynomial potentials, after removing the instability due to the annihilation of opposite charges, supermatrix models are indistinguishable from ordinary matrix models, in agreement with a recent result by Alvarez-Gaume and Manes. It is pointed out however that this may not be true for more general potentials such as for instance the supersymmetric generalization of the Penner model.Comment: 6 page

Hamiltonian Approach to 2D Dilaton-Gravities and Invariant Adm Mass

The formula existing in the literature for the ADM mass of 2D dilaton gravity is incomplete. For example, in the case of an infalling matter shockwave this formula fails to give a time-independent mass, unless a very special coordinate system is chosen. We carefully carry out the canonical formulation of 2D dilaton gravity theories (classical, CGHS and RST). As in 4D general relativity one must add a boundary term to the bulk Hamiltonian to obtain a well-defined variational problem. This boundary term coincides with the numerical value of the Hamiltonian and gives the correct mass which obviously is time-independent.Comment: revised, 12 pages, PUPT-1379; we added a reference and corrected some minor typo

Diagnostic utility of fine needle aspiration cytology in thyroid lesions

Background: Thyroid fine needle aspiration cytology (FNAC) is an important screening tool and thereby dictates clinical management. The exclusion of non-invasive follicular variant of papillary carcinoma (NIFVPTC) from thyroid malignancies and its reclassification as non-malignant entity i.e., non-invasive follicular thyroid neoplasm with papillary like nuclear features (NIFTP) has added a new dimension. Aim of this study was to study the role of fine needle aspiration cytology in screening thyroid lesions by correlation with histopathological examination and to calculate diagnostic accuracy of FNAC considering NIFTP as non-malignant and compare it with pre NIFTP era.Methods: It was an observational study done over a period of 2 years (2017-2018). It included the cases where FNAC was followed subsequently by histopathology. FNAC results were correlated with histopathological diagnosis established thereof.Results: A total of 107 patients were included in this study. Considering NIFTP as non-malignant, sensitivity, specificity, positive predictive value, negative predictive value and diagnostic accuracy were 92.97%, 100%, 100%, 92.73% and 96.23% respectively, that is significantly higher if authors considered NIFTP as malignant.Conclusions: FNAC plays an indispensable role in making preliminary diagnosis in thyroid lesions. There is a notable increase in diagnostic accuracy of FNAC in thyroid lesions and significant decrease in risk of malignancy by considering NIFTP as non-malignant

Monitoring and testing different doses of disparlure for Indian gypsy moth, Lymantria obfuscata, in a temperate region of India (Kashmir Valley)

Pheromone traps with different doses of disparlure [(Z)-7,8-epoxy-2-methyloctadecane] were tested for a local strain of the Indian gypsy moth (Lymantria obfuscata) at Sher-e-Kashmir University of Agricultural Sciences and Technology of Kashmir (India). Disparlure at 500 µg dose proved to be effective in trapping gypsy moth populations. The first adults were caught on the third week of June in 2007-2009 with peak catches a week later. Catches in disparlure-baited traps at all dosage levels (0.5, 50 and 500 µg) were significantly higher as compared to control traps. The regression equation revealed strong (99%) correlation between moth catches and applied doses. The accumulated degree day model predicted 65.31 to 117.97 heat units for larval hatch and 794.66 to 928.15 heat units for adult emergence. The principal component analysis showed significant variability between weather variables and adult L. obfuscata population

Four-dimensional BPS-spectra via M-theory

We consider the realization of four-dimensional theories with N = 2 supersymmetry as M-theory configurations including a five-brane. Our emphasis is on the spectrum of massive states, that are realized as two-branes ending on the five-brane. We start with a determination of the supersymmetries that are left unbroken by the background metric and five-brane. We then show how the central charge of the N = 2 algebra arises from the central charge associated with the M-theory two-brane. This determines the condition for a two-brane configuration to be BPS-saturated in the four-dimensional sense. By imposing certain conditions on the moduli, we can give concrete examples of such two-branes. This leads us to conjecture that vectormultiplet and hypermultiplet BPS-saturated states correspond to two-branes with the topology of a cylinder and a disc respectively. We also discuss the phenomenon of marginal stability of BPS-saturated states.Comment: 18 pages, 3 figures, uses harvmac. References adde

Dual formulation of classical W-algebras

By extending the concept of \mc, I introduce a dual formulation of (classical) nonlinear extensions of the \vir\ algebra. This dual formulation is closely related to three dimensional actions which are analogous to a \cs\ action. I present an explicit construction in terms of superfields of the $N=2$ super \wfour.Comment: (only change is an added reference), 9 pages, USC--92/01

Subcritical Superstrings

We introduce the Liouville mode into the Green-Schwarz superstring. Like massive supersymmetry without central charges, there is no kappa symmetry. However, the second-class constraints (and corresponding Wess-Zumino term) remain, and can be solved by (twisted) chiral superspace in dimensions D=4 and 6. The matter conformal anomaly is c = 4-D < 1. It thus can be canceled for physical dimensions by the usual Liouville methods, unlike the bosonic string (for which the consistency condition is c = D <= 1).Comment: 9 pg., compressed postscript file (.ps.Z), other formats (.dvi, .ps, .ps.Z, 8-bit .tex) available at http://insti.physics.sunysb.edu/~siegel/preprints/ or at ftp://max.physics.sunysb.edu/preprints/siege