Irreducible pseudo 2-factor isomorphic cubic bipartite graphs

A bipartite graph is {\em pseudo 2--factor isomorphic} if all its 2--factors have the same parity of number of circuits. In \cite{ADJLS} we proved that the only essentially 4--edge-connected pseudo 2--factor isomorphic cubic bipartite graph of girth 4 is $K_{3,3}$, and conjectured \cite[Conjecture 3.6]{ADJLS} that the only essentially 4--edge-connected cubic bipartite graphs are $K_{3,3}$, the Heawood graph and the Pappus graph. There exists a characterization of symmetric configurations $n_3$ %{\bf decide notation and how to use it in the rest of the paper} due to Martinetti (1886) in which all symmetric configurations $n_3$ can be obtained from an infinite set of so called {\em irreducible} configurations \cite{VM}. The list of irreducible configurations has been completed by Boben \cite{B} in terms of their {\em irreducible Levi graphs}. In this paper we characterize irreducible pseudo 2--factor isomorphic cubic bipartite graphs proving that the only pseudo 2--factor isomorphic irreducible Levi graphs are the Heawood and Pappus graphs. Moreover, the obtained characterization allows us to partially prove the above Conjecture

Large NN limit of irreducible tensor models: O(N)O(N) rank-33 tensors with mixed permutation symmetry

It has recently been proven that in rank three tensor models, the anti-symmetric and symmetric traceless sectors both support a large $N$ expansion dominated by melon diagrams [arXiv:1712.00249 [hep-th]]. We show how to extend these results to the last irreducible $O(N)$ tensor representation available in this context, which carries a two-dimensional representation of the symmetric group $S_3$. Along the way, we emphasize the role of the irreducibility condition: it prevents the generation of vector modes which are not compatible with the large $N$ scaling of the tensor interaction. This example supports the conjecture that a melonic large $N$ limit should exist more generally for higher rank tensor models, provided that they are appropriately restricted to an irreducible subspace.Comment: 17 pages, 7 figure

BPS States in 10+2 Dimensions

We discuss a (10+2)D N=(1,1) superalgebra and its projections to M-theory, type IIA and IIB algebras. From the complete classification of a second-rank central term valued in the so(10,2) algebra, we find all possible BPS states coming from this term. We show that, among them, there are two types of 1/2-susy BPS configurations; one corresponds to a super (2+2)-brane while another one arises from a nilpotent element in so(10,2).Comment: 31 pages, Latex, typos corrected, references adde

Towards a complete classification of fermionic symmetry protected topological phases in 3D and a general group supercohomology theory

Classification and construction of symmetry protected topological (SPT) phases in interacting boson and fermion systems have become a fascinating theoretical direction in recent years. It has been shown that the (generalized) group cohomology theory or cobordism theory can give rise to a complete classification of SPT phases in interacting boson/spin systems. Nevertheless, the construction and classification of SPT phases in interacting fermion systems are much more complicated, especially in 3D. In this work, we revisit this problem based on the equivalent class of fermionic symmetric local unitary (FSLU) transformations. We construct very general fixed point SPT wavefunctions for interacting fermion systems. We naturally reproduce the partial classifications given by special group super-cohomology theory, and we show that with an additional $\tilde{B}H^2(G_b, \mathbb Z_2)$ (the so-called obstruction free subgroup of $H^2(G_b, \mathbb Z_2)$) structure, a complete classification of SPT phases for three-dimensional interacting fermion systems with a total symmetry group $G_f=G_b\times \mathbb Z_2^f$ can be obtained for unitary symmetry group $G_b$. We also discuss the procedure of deriving a general group super-cohomology theory in arbitrary dimensions.Comment: 48 pages, 35 figures, published versio

Intersecting M-branes as Four-Dimensional Black Holes

We present two 1/8 supersymmetric intersecting p-brane solutions of 11-dimensional supergravity which upon compactification to four dimensions reduce to extremal dyonic black holes with finite area of horizon. The first solution is a configuration of three intersecting 5-branes with an extra momentum flow along the common string. The second describes a system of two 2-branes and two 5-branes. Related (by compactification and T-duality) solution of type IIB theory corresponds to a completely symmetric configuration of four intersecting 3-branes. We suggest methods for counting the BPS degeneracy of three intersecting 5-branes which, in the macroscopic limit, reproduce the Bekenstein-Hawking entropy.Comment: 15 pages, harvmac; a reference added (the version to appear in Nulcear Physics B

Symmetries of Three Harmonically-Trapped Particles in One Dimension

We present a method for solving trapped few-body problems and apply it to three equal-mass particles in a one-dimensional harmonic trap, interacting via a contact potential. By expressing the relative Hamiltonian in Jacobi cylindrical coordinates, i.e. the two-dimensional version of three-body hyperspherical coordinates, we discover an underlying ${\rm C}_{6v}$ symmetry. This symmetry simplifies the calculation of energy eigenstates of the full Hamiltonian in a truncated Hilbert space constructed from the trap Hamiltonian eigenstates. Particle superselection rules are implemented by choosing the relevant representations of ${\rm C}_{6v}$. We find that the one-dimensional system shows nearly the full richness of the three-dimensional system, and can be used to understand separability and reducibility in this system and in standard few-body approximation techniques.Comment: 27 pages, 5 figures, 6 tables, 37 references, 4 footnotes, 1 article; v2 has revised introduction and results sections as well as typos correcte

SU(3)X SU(2)XU(1) Chiral Models from Intersecting D4-/D5-branes

We clarify RR tadpole cancellation conditions for intersecting D4-/D5-branes. We find all of the D4-brane models which have D=4 three-generation chiral fermions with the SU(3)XSU(2)XU(1)^n symmetries. For the D5-brane case, we present a solution to the conditions which gives exactly the matter contents of standard model with U(1) anomalies.Comment: 6 pages, submitted to Progress Letter

pp-waves in 11-dimensions with extra supersymmetry

The Killing spinor equations for pp-wave solutions of eleven dimensional supergravity are analysed and it is shown that there are solutions that preserve 18,20,22 and 24 supersymmetries, in addition to the generic solution preserving 16 supersymmetries and the Kowalski-Glikman solution preserving 32 supersymmetries.Comment: 13 pages. Reference added, typos corrected, new examples of 7-parameter case presente