Deformed matrix models, supersymmetric lattice twists and N=1/4 supersymmetry

A manifestly supersymmetric nonperturbative matrix regularization for a twisted version of N=(8,8) theory on a curved background (a two-sphere) is constructed. Both continuum and the matrix regularization respect four exact scalar supersymmetries under a twisted version of the supersymmetry algebra. We then discuss a succinct Q=1 deformed matrix model regularization of N=4 SYM in d=4, which is equivalent to a non-commutative $A_4^*$ orbifold lattice formulation. Motivated by recent progress in supersymmetric lattices, we also propose a N=1/4 supersymmetry preserving deformation of N=4 SYM theory on $\R^4$. In this class of N=1/4 theories, both the regularized and continuum theory respect the same set of (scalar) supersymmetry. By using the equivalence of the deformed matrix models with the lattice formulations, we give a very simple physical argument on why the exact lattice supersymmetry must be a subset of scalar subalgebra. This argument disagrees with the recent claims of the link approach, for which we give a new interpretation.Comment: 47 pages, 3 figure

Relations among Supersymmetric Lattice Gauge Theories via Orbifolding

We show how to derive Catterall's supersymmetric lattice gauge theories directly from the general principle of orbifolding followed by a variant of the usual deconstruction. These theories are forced to be complexified due to a clash between charge assignments under U(1)-symmetries and lattice assignments in terms of scalar, vector and tensor components for the fermions. Other prescriptions for how to discretize the theory follow automatically by orbifolding and deconstruction. We find that Catterall's complexified model for the two-dimensional N=(2,2) theory has two independent preserved supersymmetries. We comment on consistent truncations to lattice theories without this complexification and with the correct continuum limit. The construction of lattice theories this way is general, and can be used to derive new supersymmetric lattice theories through the orbifolding procedure. As an example, we apply the prescription to topologically twisted four-dimensional N=2 supersymmetric Yang-Mills theory. We show that a consistent truncation is closely related to the lattice formulation previously given by Sugino.Comment: 20 pages, LaTeX2e, no figur

Supersymmetric Deformations of Type IIB Matrix Model as Matrix Regularization of N=4 SYM

We construct a $\mathcal{Q}=1$ supersymmetry and $U(1)^5$ global symmetry preserving deformation of the type IIB matrix model. This model, without orbifold projection, serves as a nonperturbative regularization for $\mathcal{N}=4$ supersymmetric Yang-Mills theory in four Euclidean dimensions. Upon deformation, the eigenvalues of the bosonic matrices are forced to reside on the surface of a hypertorus. We explicitly show the relation between the noncommutative moduli space of the deformed matrix theory and the Brillouin zone of the emergent lattice theory. This observation makes the transmutation of the moduli space into the base space of target field theory clearer. The lattice theory is slightly nonlocal, however the nonlocality is suppressed by the lattice spacing. In the classical continuum limit, we recover the $\mathcal{N}=4$ SYM theory. We also discuss the result in terms of D-branes and interpret it as collective excitations of D(-1) branes forming D3 branes.Comment: Version 2: Extended discussion of moduli space, added a referenc

Exact Vacuum Energy of Orbifold Lattice Theories

We investigate the orbifold lattice theories constructed from supersymmetric Yang-Mills matrix theories (mother theories) with four and eight supercharges. We show that the vacuum energy of these theories does not receive any quantum correction perturbatively.Comment: 14 pages, no figure, LaTeX2e, typos corrected, errors in references corrected, comments adde

Deconstruction and other approaches to supersymmetric lattice field theories

This report contains both a review of recent approaches to supersymmetric lattice field theories and some new results on the deconstruction approach. The essential reason for the complex phase problem of the fermion determinant is shown to be derivative interactions that are not present in the continuum. These irrelevant operators violate the self-conjugacy of the fermion action that is present in the continuum. It is explained why this complex phase problem does not disappear in the continuum limit. The fermion determinant suppression of various branches of the classical moduli space is explored, and found to be supportive of previous claims regarding the continuum limit.Comment: 70 page

Isolated interrupted inferior vena cava with azygos continuation mimicking paraesophageal lymph node enlargement

We report a case of interrupted inferior vena cava with azygos continuation diagnosed as a isolated finding in a patient with lung carcinoma. Findings of the unopacified CT scan initially simulated a paraesophageal lymphadenopathy. The contrast - enhanced spiral CT scan showed a dilated azygos vein in the absence of definable inferior vena cava

Towards lattice simulation of the gauge theory duals to black holes and hot strings

A generalization of the AdS/CFT conjecture postulates a duality between IIA string theory and 16 supercharge Yang-Mills quantum mechanics in the large N 't Hooft limit. At low temperatures string theory describes black holes, whose thermodynamics may hence be studied using the dual quantum mechanics. This quantum mechanics is strongly coupled which motivates the use of lattice techniques. We argue that, contrary to expectation, the theory when discretized naively will nevertheless recover continuum supersymmetry as the lattice spacing is sent to zero. We test these ideas by studying the 4 supercharge version of this Yang-Mills quantum mechanics in the 't Hooft limit. We use both a naive lattice action and a manifestly supersymmetric action. Using Monte Carlo methods we simulate the Euclidean theories, and study the lattice continuum limit, for both thermal and non-thermal periodic boundary conditions, confirming continuum supersymmetry is recovered for the naive action when appropriate. We obtain results for the thermal system with N up to 12. These favor the existence of a single deconfined phase for all non-zero temperatures. These results are an encouraging indication that the 16 supercharge theory is within reach using similar methods and resources.Comment: 49 pages, 14 figure

Simulations of N=2{\cal N}=2 super Yang-Mills theory in two dimensions

We present results from lattice simulations of ${\cal N}=2$ super Yang-Mills theory in two dimensions. The lattice formulation we use was developed in \cite{2dpaper} and retains both gauge invariance and an exact (twisted) supersymmetry for any lattice spacing. Results for both U(2) and SU(2) gauge groups are given. We focus on supersymmetric Ward identities, the phase of the Pfaffian resulting from integration over the Grassmann fields and the nature of the quantum moduli space.Comment: 34 pages, 12 figures, 7 tables. Eqn. 6.1 corrected. Version to be published in JHE

Induced chromosome deletions cause hypersociability and other features of Williams-Beuren syndrome in mice

The neurodevelopmental disorder Williams-Beuren syndrome is caused by spontaneous similar to 1.5 Mb deletions comprising 25 genes on human chromosome 7q11.23. To functionally dissect the deletion and identify dosage-sensitive genes, we created two half-deletions of the conserved syntenic region on mouse chromosome 5G2. Proximal deletion (PD) mice lack Gtf2i to Limk1, distal deletion (DD) mice lack Limk1 to Fkbp6, and the double heterozygotes (D/P) model the complete human deletion. Gene transcript levels in brain are generally consistent with gene dosage. Increased sociability and acoustic startle response are associated with PD, and cognitive defects with DD. Both PD and D/P males are growth-retarded, while skulls are shortened and brains are smaller in DD and D/P. Lateral ventricle (LV) volumes are reduced, and neuronal cell density in the somatosensory cortex is increased, in PD and D/P. Motor skills are most impaired in D/P. Together, these partial deletion mice replicate crucial aspects of the human disorder and serve to identify genes and gene networks contributing to the neural substrates of complex behaviours and behavioural disorders

Cooperative activation of the ATR checkpoint kinase by TopBP1 and damaged DNA

TopBP1, acting in concert with DNA containing bulky base lesions, stimulates ATR kinase activity under physiologically relevant reaction conditions. Here, we analyze the roles of the three components in ATR activation: DNA, base damage and TopBP1. We show that base adducts caused by a potent carcinogen, benzo[a]pyrene diol epoxide (BPDE), constitute a strong signal for TopBP1-dependent ATR kinase activity on Chk1 and p53. We find that the C-terminus of TopBP1 binds preferentially to damaged DNA and is sufficient to mediate damaged DNA-dependent ATR activation in a manner similar to full-length TopBP1. Significantly, we find that stimulation of ATR by BPDE-damaged DNA exhibits strong dependence on the length of DNA, with essentially no stimulation with fragments of 0.2 kb and reaching maximum stimulation with 2 kb fragments. Moreover, TopBP1 shows preferential binding to longer DNA fragments and, in contrast to previous biochemical studies, TopBP1 binding is completely independent of DNA ends. We find that TopBP1 binds to circular and linear DNAs with comparable affinities and that these DNA forms elicit the same level of TopBP1-dependent ATR activation. Taken together, these findings suggest a cooperative activation mechanism for the ATR checkpoint kinase by TopBP1 and damaged DNA