N=1 super Yang-Mills on a (3+1) dimensional transverse lattice with one exact supersymmetry

We formulate ${\cal N}$=1 super Yang-Mills theory in 3+1 dimensions on a two dimensional transverse lattice using supersymmetric discrete light cone quantization in the large-$N_c$ limit. This formulation is free of fermion species doubling. We are able to preserve one supersymmetry. We find a rich, non-trivial behavior of the mass spectrum as a function of the coupling $g\sqrt{N_c}$, and see some sort of "transition" in the structure of a bound state as we go from the weak coupling to the strong coupling. Using a toy model we give an interpretation of the rich behavior of the mass spectrum. We present the mass spectrum as a function of the winding number for those states whose color flux winds all the way around in one of the transverse directions. We use two fits to the mass spectrum and the one that has a string theory justification appears preferable. For those states whose color flux is localized we present an extrapolated value for $m^2$ for some low energy bound states in the limit where the numerical resolution goes to infinity.Comment: 23(+2 for v3) pages, 19 figures; v2: a footnote added; v3: an appendix, comments, references added. The version to appear PR

A solution to the fermion doubling problem for supersymmetric theories on the transverse lattice

Species doubling is a problem that infects most numerical methods that use a spatial lattice. An understanding of species doubling can be found in the Nielsen-Ninomiya theorem which gives a set of conditions that require species doubling. The transverse lattice approach to solving field theories, which has at least one spatial lattice, fails one of the conditions of the Nielsen-Ninomiya theorem nevertheless one still finds species doubling for the standard Lagrangian formulation of the transverse lattice. We will show that the Supersymmetric Discrete Light Cone Quantization (SDLCQ) formulation of the transverse lattice does not have species doubling.Comment: 4 pages, v2: a reference and comments added, the version to appear in Phys. Rev.

N=(1,1) Super Yang-Mills on a (2+1) Dimensional Transverse Lattice with one Exact Supersymmetry

We present a formulation of N=(1,1), Super Yang-Mills theory in 2+1 dimensions using a transverse lattice methods that exactly preserves one supersymmetry. First, using a Lagrangian approach we obtain a standard transverse lattice formulation of the Hamiltonian. We then show that the Hamiltonian also can be written discretely as the square of a supercharge and that this produces a different result. Problems associated with the discrete realization of the full supercharge algebra are discussed. Numerically we solve for the bound states of the theory in the large N_c approximation and we find good convergence. We show that the number of fermion and boson massless bound states are closely related. Also we find that this theory admits winding states in the transverse direction and that their masses vary inversely with the winding number.Comment: 16 pages, 6 figure

Improved results for N=(2,2) super Yang-Mills theory using supersymmetric discrete light-cone quantization

We consider the (1+1)-dimensional ${\cal N}=(2,2)$ super Yang--Mills theory which is obtained by dimensionally reducing ${\cal N}=1$ super Yang--Mills theory in four dimension to two dimensions. We do our calculations in the large-$N_c$ approximation using Supersymmetric Discrete Light Cone Quantization. The objective is to calculate quantities that might be investigated by researchers using other numerical methods. We present a precision study of the low-mass spectrum and the stress-energy correlator $$. We find that the mass gap of this theory closes as the numerical resolution goes to infinity and that the correlator in the intermediate $r$ region behaves like $r^{-4.75}$.Comment: 18 pages, 8 figure

Effects of the prenatal and postnatal nurturing environment on the phenotype and gut microbiota of mice with polycystic ovary syndrome induced by prenatal androgen exposure: a cross-fostering study

The gut microbiome is implicated in the pathogenesis of polycystic ovary syndrome (PCOS), and prenatal androgen exposure is involved in the development of PCOS in later life. Our previous study of a mouse model of PCOS induced by prenatal dihydrotestosterone (DHT) exposure showed that the reproductive phenotype of PCOS appears from puberty, followed by the appearance of the metabolic phenotype after young adulthood, while changes in the gut microbiota was already apparent before puberty. To determine whether the prenatal or postnatal nurturing environment primarily contributes to these changes that characterize prenatally androgenized (PNA) offspring, we used a cross-fostering model to evaluate the effects of changes in the postnatal early-life environment of PNA offspring on the development of PCOS-like phenotypes and alterations in the gut microbiota in later life. Female PNA offspring fostered by normal dams (exposed to an abnormal prenatal environment only, fostered PNA) exhibited less marked PCOS-like phenotypes than PNA offspring, especially with respect to the metabolic phenotype. The gut microbiota of the fostered PNA offspring was similar to that of controls before adolescence, but differences between the fostered PNA and control groups became apparent after young adulthood. In conclusion, both prenatal androgen exposure and the postnatal early-life environment created by the DHT injection of mothers contribute to the development of PCOS-like phenotypes and the alterations in the gut microbiota that characterize PNA offspring. Thus, both the pre- and postnatal environments represent targets for the prevention of PCOS and the associated alteration in the gut microbiota in later life