The Segal-Bargmann transform plays an important role in quantum theories of linear fields. Recently, Hall obtained a non-linear analog of this transform for quantum mechanics on Lie groups. Given a compact, connected Lie group G with its normalized Haar measure μH , the Hall transform is an isometric isomorphism from L (G,μH ) to H(GC) ∩ L2(GC, ν), where GC the complexification of G, H(GC) the ...

The study of physics beyond 4-dimensional (4D) space-time traces back to the work by Kaluza and Klein. 1) The exsitence of an extra space is essential in superstring theory 2), 3) and M -theory. 4) Recently, there is a lot of interesting research of the phenomenological and theoretical implications of an extra space with large radii based on several motivations. 5) As a feature in theories with...

A noncommutative gauge theory can be realized by considering branes in string theory with a constant NeveuSchwarz–Neveu-Schwarz ~NS-NS! two-form field @1#. In @2#, it was shown that there are two equivalent descriptions of the theory: one in terms of ordinary gauge fields Ai on a commutative space and another in terms of noncommutative gauge fields  i on a noncommutative space whose coordinate...

We present a new class of solutions in odd dimensions to Einstein’s equations containing either a positive or negative cosmological constant. These solutions resemble the even-dimensional Eguchi-Hanson(A)dS metrics, with the added feature of having Lorentzian signatures. They provide an affirmative answer to the open question as to whether or not there exist solutions with negative cosmological...

The transverse lattice 1 is an attempt to combine advantages of the light-front (LF) and lattice formulations of QCD. In this approach to QCD the time and one space direction (say x) are kept continuous, while the two ‘transverse’ directions x⊥ ≡ (x , x) are discretized. Keeping the time and x directions continuous has the advantage of preserving manifest boost invariance for boosts in the x di...

We present a six-dimensional Higgsless Standard Model with a realistic gauge sector. The model uses only the Standard Model gauge group SU(2)L × U(1)Y with the gauge bosons propagating in flat extra dimensions compactified on a rectangle. The electroweak symmetry is broken by boundary conditions, and the correct splitting between the W and Z gauge boson masses can be arranged by suitable choice...

We present a six-dimensional Higgsless Standard Model with a realistic gauge sector. The model uses only the Standard Model gauge group SU(2)L × U(1)Y with the gauge bosons propagating in flat extra dimensions compactified on a rectangle. The electroweak symmetry is broken by boundary conditions and the correct splitting between the W and Z gauge boson masses can be arranged by suitable choice ...

We present a class of N = 1 supersymmetric models of particle physics, derived directly from heterotic M-theory, that contain three families of chiral quarks and leptons coupled to the gauge group SU(3)C×SU(2)L×U(1)Y. These models are a fundamental form of “brane-world” theories, with an observable and hidden sector each confined, after compactification on a Calabi–Yau threefold, to a BPS three...

We study the moduli space of M -theories compactified on G2 manifolds which are asymptotic to a cone over quotients of S × S. We show that the moduli space is composed of several components, each of which interpolates smoothly among various classical limits corresponding to low energy gauge theories with a given number of massless U(1) factors. Each component smoothly interpolates among supersy...

We discuss the formal structure of a functional measure for Gauge Theories preserving the Slavnov-Taylor identity in the presence of Gribov horizons. Our construction defines a gauge-fixed measure in the framework of the lattice regularization by dividing the configuration space into patches with different gauge-fixing prescriptions. Taking into account the bounds described by Dell’Antonio and ...