Missing Modules, the Gnome Lie Algebra, and E10E_{10}

We study the embedding of Kac-Moody algebras into Borcherds (or generalized Kac-Moody) algebras which can be explicitly realized as Lie algebras of physical states of some completely compactified bosonic string. The extra ``missing states'' can be decomposed into irreducible highest or lowest weight ``missing modules'' w.r.t. the relevant Kac-Moody subalgebra; the corresponding lowest weights are associated with imaginary simple roots whose multiplicities can be simply understood in terms of certain polarization states of the associated string. We analyse in detail two examples where the momentum lattice of the string is given by the unique even unimodular Lorentzian lattice $II_{1,1}$ or $II_{9,1}$, respectively. The former leads to the Borcherds algebra $g_{1,1}$, which we call ``gnome Lie algebra", with maximal Kac-Moody subalgebra $A_1$. By the use of the denominator formula a complete set of imaginary simple roots can be exhibited, whereas the DDF construction provides an explicit Lie algebra basis in terms of purely longitudinal states of the compactified string in two dimensions. The second example is the Borcherds algebra $g_{9,1}$, whose maximal Kac-Moody subalgebra is the hyperbolic algebra $E_{10}$. The imaginary simple roots at level 1, which give rise to irreducible lowest weight modules for $E_{10}$, can be completely characterized; furthermore, our explicit analysis of two non-trivial level-2 root spaces leads us to conjecture that these are in fact the only imaginary simple roots for $g_{9,1}$.Comment: 31 pages, LaTeX2e, AMS packages, PSTRICK

Violation of the phase space general covariance as a diffeomorphism anomaly in quantum mechanics

We consider a topological quantum mechanics described by a phase space path integral and study the 1-dimensional analog for the path integral representation of the Kontsevich formula. We see that the naive bosonic integral possesses divergences, that it is even naively non-invariant and thus is ill-defined. We then consider a super-extension of the theory which eliminates the divergences and makes the theory naively invariant. This super-extension is equivalent to the correct choice of measure and was discussed in the literature. We then investigate the behavior of this extended theory under diffeomorphisms of the extended phase space and despite of its naive invariance find out that the theory possesses anomaly under nonlinear diffeomorphisms. We localize the origin of the anomaly and calculate the lowest nontrivial anomalous contribution.Comment: 36 page

AdS3_3 vacua and RG flows in three dimensional gauged supergravities

We study $AdS_3$ supersymmetric vacua in N=4 and N=8, three dimensional gauged supergravities, with scalar manifolds $(\frac{SO(4,4)}{SO(4)\times SO(4)})^2$ and $\frac{SO(8,8)}{SO(8)\times SO(8)}$, non-semisimple Chern-Simons gaugings $SO(4)\ltimes {\bf R}^6$ and $(SO(4)\ltimes {\bf R}^6)^2$, respectively. These are in turn equivalent to SO(4) and $SO(4)\times SO(4)$ Yang-Mills theories coupled to supergravity. For the N=4 case, we study renormalization group flows between UV and IR $AdS_3$ vacua with the same amount of supersymmetry: in one case, with (3,1) supersymmetry, we can find an analytic solution whereas in another, with (2,0) supersymmetry, we give a numerical solution. In both cases, the flows turn out to be v.e.v. flows, i.e. they are driven by the expectation value of a relevant operator in the dual $SCFT_2$. These provide examples of v.e.v. flows between two $AdS_3$ vacua within a gauged supergravity framework.Comment: 35 pages in JHEP form, 3 figures, typos corrected, references adde

Informing clients of confidentiality limits and subsequent child abuse reporting decisions: the role of dissonance

This study proposed a causal model of child abuse reporting behavior framed within cognitive dissonance theory (Festinger, 1957). It was hypothesized that the failure to provide information regarding confidentiality limits to clients would result in dissonance. Further, it was predicted that when clients subsequently disclose that they are abusing a child, clinicians\u27 dissonance would lead to behaviors associated with decreased reporting;Two hundred and forty-eight licensed psychologists from Arkansas, Connecticut, and New Mexico responded to a survey addressing the provision of confidentiality information in therapy and child abuse reporting decisions. Each respondent received a survey containing one of four vignette conditions describing a situation in which an adult client discloses information indicative of child abuse. The manipulated variables in the vignettes were severity of abuse (high and low) and provision of information regarding confidentiality limits (inform/no inform). In addition to describing their own practices in regard to informing clients of confidentiality limits, respondents rated the extent to which they might experience discomfort or dissonance (measured by a multi-item scale), how likely they would be to report the situation presented in the vignette, and how comfortable they would be with their reporting decision in the shoes of the clinician in the vignette. Other items assessed respondents\u27 perceptions of the need for agency intervention in the case, and the effects that reporting the case might have on the client\u27s treatment and on the safety of the child;Path analyses of the proposed model of reporting behavior revealed that the models did not fit the data very well overall. Failure to inform clients of limits was not directly related to decreased reporting. Additionally, hypothesized differences between conditions depicting high and low severity abuse were not supported. However, results supported the relationship between the failure to inform clients of confidentiality limits and dissonance. Further, the relation of dissonance to the belief that agency intervention could adversely affect the client\u27s treatment was supported. Implications of the findings for practitioners, as well as for future research in the area of abuse reporting decisions and, were explored

An experimental and theoretical analysis of the convected balanced arc

Convected balanced electric arcs in transverse magnetic field