Dualities in tree representations

A characterization of the tree T∗ such that BP(T∗) = ↔ DFUDS(T), the reversal of DFUDS(T) is given. An immediate consequence is a rigorous characterization of the tree T such that BP( T^) = DFUDS(T^). In summary, BP and DFUDS are unified within an encompassing framework, which might have the potential to imply future simplifications with regard to queries in BP and/or DFUDS. Immediate benefits displayed here are to identify so far unnoted commonalities in most recent work on the Range Minimum Query problem, and to provide improvements for the Minimum Length Interval Query problem

Dualities in Tree Representations

A characterization of the tree $T^*$ such that $\mathrm{BP}(T^*)=\overleftrightarrow{\mathrm{DFUDS}(T)}$, the reversal of $\mathrm{DFUDS}(T)$ is given. An immediate consequence is a rigorous characterization of the tree $\hat{T}$ such that $\mathrm{BP}(\hat{T})=\mathrm{DFUDS}(T)$. In summary, $\mathrm{BP}$ and $\mathrm{DFUDS}$ are unified within an encompassing framework, which might have the potential to imply future simplifications with regard to queries in $\mathrm{BP}$ and/or $\mathrm{DFUDS}$. Immediate benefits displayed here are to identify so far unnoted commonalities in most recent work on the Range Minimum Query problem, and to provide improvements for the Minimum Length Interval Query problem.Comment: CPM 2018, extended versio

Dualities in Tree Representations

A characterization of the tree T^* such that BP(T^*)=ova{DFUDS(T)}, the reversal of DFUDS(T) is given. An immediate consequence is a rigorous characterization of the tree T^ such that BP(T^)=DFUDS(T). In summary, BP and DFUDS are unified within an encompassing framework, which might have the potential to imply future simplifications with regard to queries in BP and/or DFUDS. Immediate benefits displayed here are to identify so far unnoted commonalities in most recent work on the Range Minimum Query problem, and to provide improvements for the Minimum Length Interval Query problem

Duality and Confinement in 3d N=2\mathcal{N}=2 "chiral" SU(N)SU(N) gauge theories

We study low-energy dynamics of three-dimensional $\mathcal{N}=2$ $SU(N)$ "chiral" gauge theories with $F$ fundamental and $\bar{F}$ anti-fundamental matters without a Chern-Simons term. Compared to a naive semi-classical analysis of the Coulomb branch, its quantum structure is highly richer than expected due to so-called "dressed" Coulomb branch (monopole) operators. We propose dualities and confinement phases for the "chiral" $SU(N)$ theories. The theories with $N>F > \bar{F}$ exhibit spontaneous supersymmetry breaking. The very many Coulomb branch operators generally remain exactly massless and are non-trivially mapped under the dualities. Some dualities lead to a novel duality between $SU(N)$ and $USp(2 \tilde{N})$ theories. For the 3d $\mathcal{N}=2$ $SU(2)$ gauge theory with $2F$ doublets, there are generally $F+2$ "chiral" and "non-chiral" dual descriptions.Comment: Appendix added, discussions added, references adde

More on N=1 Self-Dualities and Exceptional Gauge Groups

Starting from a generalization of a recent result on self-duality we systematically analyze self-dual models. We find a criterion to judge whether a given model is self-dual or not. With this tool we construct some new self-dual pairs, focussing on examples with exceptional gauge groups.Comment: 10 pages, LaTeX2e, using utarticle.cls (included

On Duality Walls in String Theory

Following the RG flow of an N=1 quiver gauge theory and applying Seiberg duality whenever necessary defines a duality cascade, that in simple cases has been understood holographically. It has been argued that in certain cases, the dualities will pile up at a certain energy scale called the duality wall, accompanied by a dramatic rise in the number of degrees of freedom. In string theory, this phenomenon is expected to occur for branes at a generic threefold singularity, for which the associated quiver has Lorentzian signature. We here study sequences of Seiberg dualities on branes at the C_3/Z_3 orbifold singularity. We use the naive beta functions to define an (unphysical) scale along the cascade. We determine, as a function of initial conditions, the scale of the wall as well as the critical exponent governing the approach to it. The position of the wall is piecewise linear, while the exponent appears to be constant. We comment on the possible implications of these results for physical walls.Comment: 22 pages, 2 figures. v2: physical interpretation rectified, reference adde

Duality between simple-group gauge theories and some applications

In this paper we investigate N=1 supersymmetric gauge theories with a product gauge group. By using smoothly confining dynamics, we can find new dualities which include higher-rank tensor fields, and in which the dual gauge group is simple, not a product. Some of them are dualities between chiral and non-chiral gauge theories. We also discuss some applications to dynamical supersymmetry breaking phenomena and new confining theories with a tree-level superpotential.Comment: 33 pages, LaTeX, references added, version to appear in PR

Supersymmetric and non-supersymmetric Seiberg-like dualities for gauged Wess-Zumino-Witten theories, realised on branes

In this work we extend the results of previous derivations of Seiberg-like dualities (level-rank duality) between gauged Wess-Zumino-Witten theories. The arguments in use to identify a potential dual for the supersymmetric WZW theory based on the coset $\frac{U(N+M)_k}{U(N)_k}$ can be extended to be applied to a wider variety of gauge groups, notably $\frac{USp(2N+2M)_{2k}}{USp(2N)_{2k}}$ and $\frac{SO(2N+2M)_{2k}}{SO(2N)_{2k}}$, which will be dealt with briefly. Most interestingly, non-supersymmetric versions of the latter theories can also be shown to have duals in a similar fashion. These results are supported by several pieces of evidence, string phenomenological interpretations of Seiberg duality, even in non-supersymmetric backgrounds, is helpful to justify the formulation, then, from field theory, quantities such as central charges or Witten indices are shown to match exactly. The stability of these non-supersymmetric models is also discussed and shown to be consistent.Comment: 3 figures, 9 table