arXiv subjects

Tristan Hubsch

Publications and source records attributed to Tristan Hubsch.

32 records · Page 2Linked to original sources

arXiv2008

$Z_7$ Orbifold Models in M-Theory

Among $T^7/Γ$ orbifold compactifications of $M$-theory, we examine models containing the particle physics Standard Model in four-dimensional spacetimes, which appear as fixed subspaces of the ten-dimensional spacetimes at each end of the interval, $I^1\simeq S^1/Z_2$, spanning the $11^\text{th}$ dimension. Using the $Z_7$ projection to break the $E_8$ gauge symmetry in each of the four-planes and a limiting relation to corresponding heterotic string compactifications, we discuss the restrictions on the possible resulting gauge field and matter spectra. In particular, some of the states are non-local: they connect two four-dimensional Worlds across the $11^\text{th}$ dimension. We illustrate our programmable calculations of the matter field spectrum, including the anomalous U(1) factor which satisfies a universal Green-Schwarz relation, discuss a Dynkin diagram technique to showcase a model with $SU(3)\times SU(2)\times U(1)^5$ gauge symmetry, and discuss generalizations to higher order orbifolds.

hep-th↗

arXiv2006

Off-shell supersymmetry and filtered Clifford supermodules

An off-shell representation of supersymmetry is a representation of the super Poincare algebra on a dynamically unconstrained space of fields. We describe such representations formally, in terms of the fields and their spacetime derivatives, and we interpret the physical concept of engineering dimension as an integral grading. We prove that formal graded off-shell representations of one-dimensional N-extended supersymmetry, i.e., the super Poincare algebra p^{1|N}, correspond to filtered Clifford supermodules over Cl(N). We also prove that formal graded off-shell representations of two-dimensional (p,q)-supersymmetry, i.e., the super Poincare algebra p^{1,1|p,q}, correspond to bifiltered Clifford supermodules over Cl(p+q). Our primary tools are the formal deformations of filtered superalgebras and supermodules, which give a one-to-one correspondence between filtered spaces and graded spaces with even degree-shifting injections. This generalizes the machinery developed by Gerstenhaber to prove that every filtered algebra is a deformation of its associated graded algebra. Our treatment extends Gerstenhaber's discussion to the case of filtrations which are compatible with a supersymmetric structure, as well as to filtered modules in addition to filtered algebras. We also describe the analogous constructions for bifiltrations and bigradings.

math-ph↗

arXiv2004

From Quantum To Classical Dynamics: A Landau Continuous Phase Transition With Spontaneous Superposition Breaking

Developing an earlier proposal (Ne'eman, Damnjanovic, etc), we show herein that there is a Landau continuous phase transition from the exact quantum dynamics to the effectively classical one, occurring via spontaneous superposition breaking (effective hiding), as a special case of the corresponding general formalism (Bernstein). Critical values of the order parameters for this transition are determined by Heisenberg's indeterminacy relations, change continuously, and are in excellent agreement with the recent and remarkable experiments with Bose condensation. It is also shown that such a phase transition can sucessfully model self-collapse (self-decoherence), as an effective classical phenomenon, on the measurement device. This then induces a relative collapse (relative decoherence) as an effective quantum phenomenon on the measured quantum object by measurement. We demonstrate this (including the case of Bose-Einstein condensation) in the well-known cases of the Stern-Gerlach spin measurement, Bell's inequality and the recently discussed quantum superposition on a mirror a la Marshall et al. These results provide for a proof that quantum mechanics, in distinction to all absolute collapse and hidden-variable theories, is local and objective. There now appear no insuperable obstacles to solving the open problems in quantum theory of measurement and foundation of quantum mechanics, and strictly within the standard quantum-mechanical formalism. Simply put, quantum mechanics is a field theory over the Hilbert space, the classical mechanics characteristics of which emerge through spontaneous superposition breaking.

quant-ph↗

arXiv2002

On the Geometry and Homology of Certain Simple Stratified Varieties

We study certain mild degenerations of algebraic varieties which appear in the analysis of a large class of supersymmetric theories, including superstring theory. We analyze Witten's sigma-model and find that the non-transversality of the superpotential induces a singularization and stratification of the ground state variety. This stratified variety (the union of the singular ground state variety and its exo-curve strata) admit homology groups which, excepting the middle dimension, satisfy the "Kahler package" of requirements, extend the "flopped" pair of small resolutions to an "(exo)flopped" triple, and is compatible with mirror symmetry and string theory. Finally, we revisit the conifold transition as it applies to our formalism.

math.AG↗

arXiv2000

Yang-Mills and Supersymmetry Covariance Must Coexist

Supersymmetry and Yang-Mills type gauge invariance are two of the essential properties of most, and possibly the most important models in fundamental physics. Supersymmetry is nearly trivial to prove in the (traditionally gauge-noncovariant) superfield formalism, whereas the gauge-covariant formalism makes gauge invariance manifest. In 3+1-dimensions, the transformation from one into the other is elementary and essentially unique. By contrast, this transformation turns out to be impossible in the most general 1+1-dimensional case. In fact, only the (manifestly) gauge- and supersymmetry-covariant formalism guarantees both universal gauge-invariance and supersymmetry.

hep-th↗

arXiv1999

Gauging Yang-Mills Symmetries In 1+1-Dimensional Spacetime

We present a systematic and 'from the ground up' analysis of the 'minimal coupling' type of gauging of Yang-Mills symmetries in (2,2)-supersymmetric 1+1-dimensional spacetime. Unlike in the familiar 3+1-dimensional N=1 supersymmetric case, we find several distinct types of minimal coupling symmetry gauging, and so several distinct types of gauge (super)fields, some of which entirely novel. Also, we find that certain (quartoid) constrained superfields can couple to no gauge superfield at all, others (haploid ones) can couple only very selectively, while still others (non-minimal, i.e., linear ones) couple universally to all gauge superfields.

hep-th↗

arXiv1999

Linear and Chiral Superfields are Usefully Inequivalent

Chiral superfields have been used, and extensively, almost ever since supersymmetry has been discovered. Complex linear superfields afford an alternate representation of matter, but are widely misbelieved to be 'physically equivalent' to chiral ones. We prove the opposite is true. Curiously, this re-enables a previously thwarted interpretation of the low-energy (super)field limit of superstrings.

hep-th↗

arXiv1999

Some Algebraic Symmetries of (2,2)-Supersymmetric Systems

The Hilbert spaces of supersymmetric systems admit symmetries which are often related to the topology and geometry of the (target) field-space. Here, we study certain (2,2)-supersymmetric systems in 2-dimensional spacetime which are closely related to superstring models. They all turn out to posess some hitherto unexploited and geometrically and topologically unobstructed symmetries, providing new tools for studying the topology and geometry of superstring target spacetimes, and so the dynamics of the effective field theory in these.

hep-th↗

arXiv1999

Haploid (2,2)-Superfields In 2-Dimensional Spacetime

Superfields in 2-dimensional (2,2)-superspacetime which are independent of (some) half of the fermionic coordinates are discussed in a hopefully both comprehensive and comprehensible manner. An embarrassing abundance of these simplest `building blocks' makes it utterly impossible to write down the `most general Lagrangian'. With some ad hoc but perhaps plausible restrictions, a rather general Lagrangian is found, which exhibits many of the phenomena that have been studied recently, and harbors many more. In particular, it becomes patently obvious that the (2,2)-supersymmetric 2-dimensional field theory target space geometries (many of which are suitable for (super)string propagation) are far more general than Kahler manifolds with holomorphic bundles.

hep-th↗

arXiv1999

CNM Models, Holomorphic Functions and Projective Superspace C-Maps

Continuing the investigation of CNM (chiral-nonminimal) hypermultiplet nonlinear sigma-models, we propose extensions of the concept of the c-map which relate holomorphic functions to hyper-Kahler geometries. In particular, we show that a whole series of hyper-Kahler potentials can be derived by replacing the role of the 4D, N = 1 tensor multiplet in the original c-map by 4D, N = 1 non-minimal multiplets and auxiliary superfields. The resulting N = 2 models appear to have interesting connections to Calabi-Yau manifolds and algebraic varieties. These models also emphasize the fact that special hyper-Kahler manifolds (the analogs of special Kahler manifolds) without isometries exist.

hep-th↗

arXiv1998

A Fermionic Hodge Star Operator

A fermionic analogue of the Hodge star operation is shown to have an explicit operator representation in models with fermions, in spacetimes of any dimension. This operator realizes a conjugation (pairing) not used explicitly in field-theory, and induces a metric in the space of wave-function(al)s just as in exterior calculus. If made real (Hermitian), this induced metric turns out to be identical to the standard one constructed using Hermitian conjugation; the utility of the induced complex bilinear form remains unclear.

hep-th↗

arXiv1996

On A Stringy Singular Cohomology

String theory has already motivated, suggested, and sometimes well-nigh proved a number of interesting and sometimes unexpected mathematical results, such as mirror symmetry. A careful examination of the behavior of string propagation on (mildly) singular varieties similarly suggests a new type of (co)homology theory. It has the `good behavior' of the well established intersection (co)homology and $L^2$-cohomology, but is markedly different in some aspects. For one, unlike the intersection (co)homology and the $L^2$-cohomology (or any other known thus far), this new cohomology is symmetric with respect to the mirror map. Among the available choices, this makes it into a prime candidate for describing the string theory zero modes in geometrical terms.

hep-th↗

arXiv1993

Periods for Calabi--Yau and Landau--Ginzburg Vacua

The complete structure of the moduli space of \cys\ and the associated Landau-Ginzburg theories, and hence also of the corresponding low-energy effective theory that results from (2,2) superstring compactification, may be determined in terms of certain holomorphic functions called periods. These periods are shown to be readily calculable for a great many such models. We illustrate this by computing the periods explicitly for a number of classes of \cys. We also point out that it is possible to read off from the periods certain important information relating to the mirror manifolds.

hep-th↗

arXiv1993

Spacetime Variable Superstring Vacua

In a general superstring vacuum configuration, the `internal' space (sector) varies in spacetime. When this variation is non-trivial only in two space-like dimensions, the vacuum contains static cosmic strings with finite energy per unit length and which is, up to interactions with matter, an easily computed topological invariant. The total spacetime is smooth although the `internal' space is singular at the center of each cosmic string. In a similar analysis of the Wick-rotated Euclidean model, these cosmic strings acquire expected self-interactions. Also, a possibility emerges to define a global time in order to rotate back to the Lorentzian case.

hep-th↗