Two Loop Renormalization of Massive (p,q) Supersymmetric Sigma Models

We calculate the beta-functions of the general massive (p,q) supersymmetric sigma model to two loop order using (1,0) superfields. The conditions for finiteness are discussed in relation to (p,q) supersymmetry. We also calculate the effective potential using component fields to one loop order and consider the possibility of perturbative breaking of supersymmetry. The effect of one loop finite local counter terms and the ultra-violet behaviour of the off-shell (p,q) models to all orders in perturbation theory are also addressed.Comment: 43 pages phyzzx with 5 figure

Heterotic non-linear sigma models with anti-de Sitter target spaces

We calculate the beta function of non-linear sigma models with S^{D+1} and AdS_{D+1} target spaces in a 1/D expansion up to order 1/D^2 and to all orders in \alpha'. This beta function encodes partial information about the spacetime effective action for the heterotic string to all orders in \alpha'. We argue that a zero of the beta function, corresponding to a worldsheet CFT with AdS_{D+1} target space, arises from competition between the one-loop and higher-loop terms, similarly to the bosonic and supersymmetric cases studied previously in hep-th/0512355. Various critical exponents of the non-linear sigma model are calculated, and checks of the calculation are presented.Comment: 36 pages, 7 figure

Ultraviolet properties of noncommutative non-linear sigma-models in two dimensions

We discuss the ultra-violet properties of bosonic and supersymmetric noncommutative non-linear sigma-models in two dimensions, both with and without a Wess-Zumino-Witten term.Comment: 10 pages, including 1 figure. Plain TeX. Uses Harvmac and epsf. Minor revisions and additional reference. Version to be published in Phys. Lett.

Exact Bosonic and Supersymmetric String Black Hole Solutions

We show that Witten's two-dimensional string black hole metric is exactly conformally invariant in the supersymmetric case. We also demonstrate that this metric, together with a recently proposed exact metric for the bosonic case, are respectively consistent with the supersymmetric and bosonic $\sigma$-model conformal invariance conditions up to four-loop order.Comment: 14

On Anomaly-free Supergravity as an Effective String Theory

The equations of motion of anomaly-free supergravity are shown to fulfil (to all orders in $\alpha'$) a differential condition corresponding to the one relating the Weyl anomaly coefficients for a non-linear sigma model representing a (heterotic) string propagating in a non-trivial background. This supports the possibility that anomaly-free supergravity could provide the complete massless effective theory for the heterotic string.Comment: 7 pages, Latex, CERN-TH.6686/9

The Rat Lux Actuating Search Task (LAST) and Effects of Sleep Deprivation on Task Reversal Performance

The article of record as published may be found at�https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4124170Sleep deprivation (SD) causes significant deficits in multiple aspects of cognition, including sustained attention and working memory. Investigating the neural processes underpinning these cognitive losses has proven challenging due to the confounds of current animal tasks; many employ appetitive or aversive stimuli to motivate behavior, while others lack task complexity that translates to human studies of executive function. We established the Lux Actuating Search Task (LAST) to circumvent these issues. The LAST is performed in a circular, open-field arena that requires rats to find an unmarked, quasi-randomly positioned target. Constant low-level floor vibrations motivate ambulation, while light intensity (determined by the rodent's proximity to the target destination) provides continuous visual feedback. The task has two paradigms that differ based on the relationship between the light intensity and target proximity: the Low Lux Target (LLT) paradigm and the High Lux Target paradigm (HLT). In this study, on days 1 to 6, the rats completed nine trials per day on one of the two paradigms. On day 7, the rats were either sleep deprived by gentle handling or were left undisturbed before undertaking the opposite (reversal) paradigm on days 7 to 9. Our results showed that SD significantly impeded the ability of Long Evans rats to learn the reversal paradigm, as indicated by increased times to target and increased failure percentages compared to rats whose sleep was undisturbed. Rats also showed reduced learning with the HLT paradigm, as the initial task or as the reversal task, likely due to the rodents' photophobia limiting their motivation to navigate toward a bright light, which is required to succeed

O(d,d) invariance at two and three loops

We show that in a two-dimensional sigma-model whose fields only depend on one target space co-ordinate, the O(d,d) invariance of the conformal invariance conditions observed at one loop is preserved at two loops (in the general case with torsion) and at three loops (in the case without torsion).Comment: 21 pages. Plain Tex. Uses Harvmac ("b" option). Revised Version with references added and minor errors correcte

Finiteness and anomalies in (4,0) supersymmetric sigma models

Power-counting arguments based on extended superfields have been used to argue that two-dimensional supersymmetric sigma models with (4,0) supersymmetry are finite. This result is confirmed up to three loop order in pertubation theory by an explicit calculation using (1,0) superfields. In particular, it is shown that the finite counterterms which must be introduced into the theory in order to maintain (4,0) supersymmetry are precisely the terms that are required to establish ultra-violet finiteness.Comment: 19 page

Heterotic string solutions and coset conformal field theories

We discuss solutions of the heterotic string theory which are analogous to bosonic and superstring backgrounds related to coset conformal field theories. A class of exact `left-right symmetric' solutions is obtained by supplementing the metric, antisymmetric tensor and dilaton of the superstring solutions by the gauge field background equal to the generalised Lorentz connection with torsion. As in the superstring case, these backgrounds are \a'-independent, i.e. have a `semiclassical' form. The corresponding heterotic string sigma model is obtained from the combination of the (1,0) supersymmetric gauged WZNW action with the action of internal fermions coupled to the target space gauge field. The pure (1,0) supersymmetric gauged WZNW theory is anomalous and does not describe a consistent heterotic string solution. We also find (to the order $\alpha'^3$) a two-dimensional perturbative heterotic string solution with the trivial gauge field background. To the leading order in $\alpha'$ it coincides with the known $SL(2,R)/U(1)$ bosonic or superstring solutions. This solution does not correspond to a `heterotic' combination of the left superstring and right bosonic $L_0$-operators at the conformal field theory level. Some duality properties of the heterotic string solutions are studied.Comment: 28 pages, harvmac (b), CERN-TH.6872/93, RI-150-9

A class of finite two - dimensional sigma models and string vacua

We consider a two - dimensional Minkowski signature sigma model with a $2+N$ - dimensional target space metric having a null Killing vector. It is shown that the model is finite to all orders of the loop expansion if the dependence of the ``transverse" part of the metric \ggij (u,x) on the light cone coordinate $u$ is subject to the standard renormalization group equation of the $N$ - dimensional sigma model, {d\ggij\over du} = \gb_{ij} =R_{ij} + ... . In particular, we discuss the `one - coupling' case when \ggij(u,x) is a metric of an $N$ - dimensional symmetric space \gij(x) multiplied by a function $f(u)$. The theory is finite if $f(u)$ is equal to the ``running" coupling of the symmetric space sigma model (with $u$ playing the role of the RG ``time"). For example, the geometry of space - time with \gij being the metric of the $N$ - sphere is determined by the form of the \gb - function of the $O(N+1)$ model. The ``asymptotic freedom" limit of large $u$ corresponds to the weak coupling limit of small $2+N$ - dimensional curvature. We prove that there exists a dilaton field which together with the $2+N$ - dimensional metric solves the sigma model Weyl invariance conditions. The resulting backgrounds thus represent new tree level string vacua. We also remark on possible connections with some $2d$ quantum gravity models.Comment: 15 pages [Complete revision. The main statement of the previous version is generalised to the case of an arbitrary ``transverse" metric satisfying sigma model renormalization group equation.