Intersecting brane models and F-theory in six dimensions

We analyze six-dimensional supergravity theories coming from intersecting brane models on the toroidal orbifold T⁴/_Z2$T^4/{\mathbb{Z}}_2$. We use recently developed tools for mapping general 6D supergravity theories to F-theory to identify F-theory constructions dual to the intersecting brane models. The F-theory picture illuminates several aspects of these models. In particular, we have some new insight into the matter spectrum on intersecting branes, and analyze gauge group enhancement as branes approach orbifold points. These novel features of intersecting brane models are also relevant in four dimensions, and are confirmed in 6D using more standard Chan–Paton methods.     

Gauge coupling flux thresholds, exotic matter and the unification scale in F-SU(5) GUT

We explore the gauge coupling relations and the unification scale in F-theory SU(5) GUT broken down to the Standard Model by an internal U(1) _Y gauge flux. We consider variants with exotic matter representations which may appear in these constructions and investigate their rôle in the effective field theory model. We make a detailed investigation on the conditions imposed on the extraneous matter to raise the unification scale and make the color triplets heavy in order to avoid fast proton decay. We also discuss in brief the implications on the gaugino masses.     

Superalgebras in N = 1 gauge theories

N = 1 supersymmetric gauge theories with global flavor symmetries contain a gauge invariant W-superalgebra which acts on its moduli space of gauge invariants. With adjoint matter, this superalgebra reduces to a graded Lie algebra. When the gauge group is SO(n_c), with vector matter, it is a W-algebra, and the primary invariants form one of its representation. The same superalgebra exists in the dual theory, but its construction in terms of the dual fields suggests that duality may be understood in terms of a charge conjugation within the algebra. We extend the analysis to the gauge group E₆.     

The structure of the Yang–Mills spectrum for arbitrary simple gauge algebras

The mass spectrum of pure Yang–Mills theory in 3+1 dimensions is discussed for an arbitrary simple gauge algebra within a quasigluon picture. The general structure of the low-lying gluelump and two-quasigluon glueball spectrum is shown to be common to all algebras, while the lightest C=− three-quasigluon glueballs only exist when the gauge algebra is A _r≥2, that is, in particular, \mathfraksu(N 3 3)\mathfrak{su}(N\geq3). Higher-lying C=− glueballs are shown to exist only for the A _r≥2, D_odd−r≥4 and E₆ gauge algebras. The shape of the static energy between adjoint sources is also discussed assuming the Casimir scaling hypothesis and a funnel form; it appears to be gauge-algebra dependent when at least three sources are considered. As a main result, the present framework’s predictions are shown to be consistent with available lattice data in the particular case of an \mathfraksu(N)\mathfrak{su}(N) gauge algebra within ’t Hooft’s large-N limit.     

Enhanced Gauge Symmetry and Braid Group Actions

 Enhanced gauge symmetry appears in Type II string theory (as well as F- and M-theory) compactified on Calabi–Yau manifolds containing exceptional divisors meeting in Dynkin configurations. It is shown that in many such cases, at enhanced symmetry points in moduli a braid group acts on the derived category of sheaves of the variety. This braid group covers the Weyl group of the enhanced symmetry algebra, which itself acts on the deformation space of the variety in a compatible way. Extensions of this result are given for nontrivial B-fields on K3 surfaces, explaining physical restrictions on the B-field, as well as for elliptic fibrations. The present point of view also gives new evidence for the enhanced gauge symmetry content in the case of a local A _2n -configuration in a threefold having global ℤ/2 monodromy. Received: 28 October 2002 / Accepted: 9 December 2002 Published online: 28 May 2003 Communicated by R.H. Dijkgraaf     

String Geometry and the Noncommutative Torus

We construct a new gauge theory on a pair of d-dimensional noncommutative tori. The latter comes from an intimate relationship between the noncommutative geometry associated with a lattice vertex operator algebra ? and the noncommutative torus. We show that the tachyon algebra of ? is naturally isomorphic to a class of twisted modules representing quantum deformations of the algebra of functions on the torus. We construct the corresponding real spectral triples and determine their Morita equivalence classes using string duality arguments. These constructions yield simple proofs of the O(d,d;ℤ) Morita equivalences between d-dimensional noncommutative tori and give a natural physical interpretation of them in terms of the target space duality group of toroidally compactified string theory. We classify the automorphisms of the twisted modules and construct the most general gauge theory which is invariant under the automorphism group. We compute bosonic and fermionic actions associated with these gauge theories and show that they are explicitly duality-symmetric. The duality-invariant gauge theory is manifestly covariant but contains highly non-local interactions. We show that it also admits a new sort of particle-antiparticle duality which enables the construction of instanton field configurations in any dimension. The duality non-symmetric on-shell projection of the field theory is shown to coincide with the standard non-abelian Yang–Mills gauge theory minimally coupled to massive Dirac fermion fields. Received: 26 October 1998/ Accepted: 9 April 1999     

Study of single weak boson production in electron-positron scattering

The studies of the week boson production in electron-positron scattering are reviewed. At the lowest order of the Weinberg-Salam gauge theory, the cross sections for the various processes of the single weak boson production are computed by paying an attention on the gauge invariance at the high energies, or by calculating all the relevant Feynman diagrams, some of which have been neglected in the studies so far. A formulation is presented to compute the cross sections for the various processes,e ⁺ e ^?→WUD, whereW is the weak boson,WUD stands for \(W^ + \bar U D\) , or \(W^ - U \bar D\) , andU(D) represents the up (down) state of theSU(2) _L doublet. Also the upper bound of the contributions from the single weak boson production via the two photon process is estimated by using the real photon approximation.     

Gauge theory of gravitational interaction of macroscopic matter

Within the framework of the gauge theory of gravitation as a gauge theory of the local group P₄ × D (Poincaré and dilatation), the gravitational interaction of a continuous medium in Weil space, in which the Weil nonmetricity is due to localization of the dilatation group, and its source is the mass flux density of matter, i.e., its dilatational current, is considered. Using the variational principle, with the curvature scalar in Weil space as the geometric Lagrangian, dynamic equations of the theory are obtained, and the corresponding accurate solutions are found.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 81–83, July, 1991.     

Algebra of Deformed Differential Operators and Induced Integrable Toda Field Theory

We build in this paper the algebra of q-deformed pseudo-differential operators, shown to be an essential step toward setting a q-deformed integrability program. In fact, using the results of this q-deformed algebra, we derive the q-analogues of the generalized KdV hierarchy. We focus in particular on the first leading orders of this q-deformed hierarchy, namely the q-KdV and q-Boussinesq integrable systems. We also present the q-generalization of the conformal transformations of the currents u _n ,n 2, and discuss the primary condition of the fields W _n , n 2, by using the Volterra gauge group transformations for the q-covariant Lax operators. An induced su(n)-Toda(su(2)-Liouville) field theory construction is discussed and other important features are presented.     

Kähler metrics and gauge kinetic functions for intersecting D6‐branes on toroidal orbifolds – The complete perturbative story

We systematically derive the perturbatively exact holomorphic gauge kinetic function, the open string Kähler metrics and closed string Kähler potential on intersecting D6‐branes by matching open string one‐loop computations of gauge thresholds with field theoretical gauge couplings in 𝒩 = 1 supergravity. We consider all cases of bulk, fractional and rigid D6‐branes on T⁶/Ω ℛ and the orbifolds T⁶/(ℤ_N × Ω ℛ) and T⁶/(ℤ₂ × ℤ_2M × Ω ℛ) without and with discrete torsion, which differ in the number of bulk complex structures and in the bulk Kähler potential. Our analysis includes all supersymmetric configurations of vanishing and non‐vanishing angles among D6‐branes and O6‐planes, and all possible Wilson line and displacement moduli are taken into account. The shape of the Kähler moduli turns out to be orbifold independent but angle dependent, whereas the holomorphic gauge kinetic functions obtain three different kinds of one‐loop corrections: a Kähler moduli dependent one for some vanishing angle independently of the orbifold background, another one depending on complex structure moduli only for fractional and rigid D6‐branes, and finally a constant term from intersections with O6‐planes. These results are of essential importance for the construction of the related effective field theory of phenomenologically appealing D‐brane models. As first examples, we compute the complete perturbative gauge kinetic functions and Kähler metrics for some T⁶/ℤ₂ × ℤ₂ examples with rigid D‐branes of [1]. As a second class of examples, the Kähler metrics and gauge kinetic functions for the fractional QCD and leptonic D6‐brane stacks of the Standard Model on T⁶/ℤ₆^′T⁶/ℤ₆^′ from [2] are given.     

Single weak boson production in electron-positron annihilation

The cross sections for the process,e ⁺ e ^?→W ^±+hadrons are estimated extensively at the lowest order in the minimal gauge theory ofSU(2) _L ×U(1). It is pointed out that our result on the angular distribution is not compatible with the result reported by Neufeld.     

O(5)×U(1) electroweak gauge theory and the neutrino oscillations in matter

A study is made of the groupO(5)×U(1). The group is economical in the number of gauge bosons, which we associate with each of its generators, and is anomaly-free. The left-handed leptonsL _L ^T (v _e ,e,,v ) _L are assigned to the four-dimensional spinorial representations ofO(5). The right-handed particles are taken to be the singlets of the group. The theory has three sets of gauge bosons: (1) analogues of the GWS model, (2) additional charged gauge bosons, and (3) a set of three additional neutral gauge bosons as compared to the GWS model. We introduce neutrino mixing by mixing the additional charged gauge bosons. We develope a theory of neutrino oscillations in matter in such a way that in the absence of matter the scattering length reduces to the usual scattering length in vacuum. Even if the neutrino masses are equal or the neutrinos are massless, we still have neutrino oscillations in matter, a result already noted by Wolfenstein.     

Operator-valued connections,Lie connections,and Gauge field theory

Noether's first theorem tells us that the global symmetry groupG _r of an action integral is a Lie group of point transformations that acts on the Cartesian product of the space-time manifold with the space of states and their derivatives. Gauge theory constructs are thus required for symmetry groups that act indiscriminately on the independent and dependent variables where the group structure can not necessarily be realized as a subgroup of the general linear group. Noting that the Lie algebra of a general symmetry groupG _r can be realized as a Lie algebrag _r of Lie derivatives on an appropriately structured manifold,G _r -covariant derivatives are introduced through study of connection 1-forms that take their values in the Lie algebrag _r of Lie derivatives (operator-valued connections). This leads to a general theory of operator-valued curvature 2-forms and to the important special class of Lie connections. The latter are naturally associated with the minimal replacement and minimal coupling constructs of gauge theory when the symmetry groupG _r is allowed to act locally. Lie connections give rise to the gauge fields that compensate for the local action ofG _r in a natural way. All governing field equations and their integrability conditions are derived for an arbitrary finite dimensional Lie group of symmetries. The case whereG _r contains the ten-parameter Poincaré group on a flat space-timeM ₄ is considered. The Lorentz structure ofM ₄ is shown to give a pseudo-Riemannian structure of signature 2 under the minimal replacement associated with the Lie connection of the local action of the Poincaré group. Field equations for the matter fields and the gauge fields are given for any system of matter fields whose action integral is invariant under the global action of the Poincaré group.     

On a microscopic representation of space-time

We start from a noncompact Lie algebra isomorphic to the Dirac algebra and relate this Lie algebra in a brief review to low-energy hadron physics described by the compact group SU(4). This step permits an overall physical identification of the operator actions. Then we discuss the geometrical origin of this noncompact Lie algebra and ??reduce?? the geometry in order to introduce in each of these steps coordinate definitions which can be related to an algebraic representation in terms of the spontaneous symmetry breakdown along the Lie algebra chain su*(4) ?? usp(4) ?? su(2) × u(1). Standard techniques of Lie algebra decomposition(s) as well as the (physical) operator identification give rise to interesting physical aspects and lead to a rank-1 Riemannian space which provides an analytic representation and leads to a 5-dimensional hyperbolic space H ₅ with SO(5, 1) isometries. The action of the (compact) symplectic group decomposes this (globally) hyperbolic space into H ₂ ?? H ₃ with SO(2, 1) and SO(3, 1) isometries, respectively, which we relate to electromagnetic (dynamically broken SU(2) isospin) and Lorentz transformations. Last not least, we attribute this symmetry pattern to the algebraic representation of a projective geometry over the division algebra H and subsequent coordinate restrictions.     

Lattice study of dense matter with two colors and four flavors

We present results from a simulation of SU(2) lattice gauge theory with N _f = 4 flavors of Wilson fermion and non-zero quark chemical potential μ, using the same 12³×24 lattice, bare gauge coupling, and pion mass in cut-off units as a previous study (S. Hands, S. Kim, J.I. Skullerud, Phys. Rev. D 81, 091502(R) (2010)) with N _f = 2 . The string tension for N _f = 4 is found to be considerably smaller implying smoother gauge field configurations. Thermodynamic observables and order parameters for superfluidity and color deconfinement are studied, and comparisons drawn between the two theories. Results for quark density and pressure as functions of μ are qualitatively similar for N _f = 2 and N _f = 4 ; in both cases there is evidence for a phase in which baryonic matter is simultaneously degenerate and confined. Results for the stress-energy tensor, however, suggest that while N _f = 2 has a regime where dilute matter is non-relativistic and weakly interacting, N _f = 4 matter is relativistic and strongly interacting for all values of μ above onset.     

Area-preserving diffeomorphisms and higher-spin algebras

We show that there exists a one-parameter family of infinite-dimensional algebras that includes the bosonicd=3 Fradkin-Vasiliev higher-spin algebra and the non-Euclidean version of the algebra of area-preserving diffeomorphisms of the two-sphereS ² as two distinct members. The non-Euclidean version of the area preserving algebra corresponds to the algebra of area-preserving diffeomorphisms of the hyperbolic spaceS ^1,1, and can be rewritten as . As an application of our results, we formulate a newd=2+1 massless higher-spin field theory as the gauge theory of the area-preserving diffeomorphisms ofS ^1,1.     

Octonionic Non-Abelian Gauge Theory

We have made an attempt to describe the octonion formulation of Abelian and non-Abelian gauge theory of dyons in terms of 2×2 Zorn vector matrix realization. As such, we have discussed the U(1) _e ×U(1) _m Abelian gauge theory and U(1)×SU(2) electroweak gauge theory and also the SU(2) _e ×SU(2) _m non-Abelian gauge theory in term of 2×2 Zorn vector matrix realization of split octonions. It is shown that SU(2) _e characterizes the usual theory of the Yang Mill’s field (isospin or weak interactions) due to presence of electric charge while the gauge group SU(2) _m may be related to the existence of ’t Hooft-Polyakov monopole in non-Abelian Gauge theory. Accordingly, we have obtained the manifestly covariant field equations and equations of motion.     

Measuring of mass and spin of dark matter particles at ILC

In many models stability of dark matter particles D (with mass M _D ) is ensured by a new conserved quantum number which we call the D-parity. We consider models which also contain charged D-odd particle D ^± (with mass M _±). We study the process e ⁺ e ^? ?? D ⁺ D ^? followed by decay of D ^± to D and gauge bosons W (either on-shell or off-shell). Measuring the end points of the energy distribution of W??s would determine M _D and M ^±. However, the hadron mode of W decay would lead to low precision in this measurement. while the information from the lepton mode looks incomplete. I show that it is sufficient to measure the energy distribution of a single lepton (for definiteness ??) in the process e ⁺ e ^? ?? ?? + 2jets + large missing E _T . The well identified singularities in this distribution allow for determination of M _D and M _± with a high precision. After that, measuring the corresponding cross section will allow one to determine the spin of D particles.