Internal symmetry currents and supersymmetric effective lagrangians

A supersymmetric and non-linearly realized internally symmetric action is constructed from the super Kähler potential of Goldstone scalar superfields. Noether's theorem in superspace is derived and the associated superfield of currents defined. The currents are used to derive a super Dashen formula relating the (quasi) Goldstone masses and decay constants to the symmetry breaking part of the theory and to supersymmetrically gauge the invariant subgroup as well as the full group.     

Green functions in a super self-dual Yang-Mills background

In euclidean supersymmetric theories of chiral superfields and vector superfields coupled to a super-self-dual Yang-Mills background, we define Green functions for the Laplace-type differential operators which are obtained from the quadratic part of the action. These Green functions are expressed in terms of the Green function on the space of right chiral superfields, and an explicit expression for the right chiral Green function in the fundamental representation of an SU(n) gauge group is presented using the supersymmetric version of the ADHM formalism. The superfield kernels associated with the Laplace-type operators are used to obtain the one-loop quantum corrections to the super-self-dual Yang-Mills action, and also to provide a superfield version of the super-index theorems for the components of chiral superfields in a self-dual background.     

Gauge theory in deformed $$ \mathcal{N} $$ = (1, 1) superspace

We review the non-anticommutative Q-deformations of = (1, 1) supersymmetric theories in four-dimensional Euclidean harmonic superspace. These deformations preserve chirality and harmonic Grassmann analyticity. The associated field theories arise as a low-energy limit of string theory in specific backgrounds and generalize the Moyal-deformed supersymmetric field theories. A characteristic feature of the Q-deformed theories is the half-breaking of supersymmetry in the chiral sector of the Euclidean superspace. Our main focus is on the chiral singlet Q-deformation, which is distinguished by preserving the SO(4) ∼ Spin(4) “Lorentz” symmetry and the SU(2) R-symmetry. We present the superfield and component structures of the deformed = (1, 0) supersymmetric gauge theory as well as of hypermultiplets coupled to a gauge superfield: invariant actions, deformed transformation rules, and so on. We discuss quantum aspects of these models and prove their renormalizability in the Abelian case. For the charged hypermultiplet in an Abelian gauge superfield background we construct the deformed holomorphic effective action. The text was submitted by the authors in English.     

Augmented superfield approach to exact nilpotent symmetries for matter fields in non-Abelian theory

We derive the nilpotent (anti-) BRST symmetry transformations for the Dirac (matter) fields of an interacting four (3+1)-dimensional 1-form non-Abelian gauge theory by applying the theoretical arsenal of augmented superfield formalism where (i) the horizontality condition, and (ii) the equality of a gauge invariant quantity, on the six (4,2)-dimensional supermanifold, are exploited together. The above supermanifold is parameterized by four bosonic spacetime coordinates x^μ (with μ=0,1,2,3) and a couple of Grassmannian variables θ and θ̄. The on-shell nilpotent BRST symmetry transformations for all the fields of the theory are derived by considering the chiral superfields on the five (4,1)-dimensional super sub-manifold and the off-shell nilpotent symmetry transformations emerge from the consideration of the general superfields on the full six (4,2)-dimensional supermanifold. Geometrical interpretations for all the above nilpotent symmetry transformations are also discussed within the framework of augmented superfield formalism.     

On equal constituent quark masses in different heavy quarkonia potential models

An Azcarraga-Lukierski supersymmetric particle model, which is invariant with respect to theN=2 extended SuperPoincare group, is quantised by the method of Dirac brackets. The central charges, which satisfy the spin reducing conditions, are conjugate to additional bosonic coordinates in the superspace. The resulting superwavefunction doublet is in one-to-one correspondence with the superfield expansion of Sohnius describing the Fayet hypermultiplet.     

Superprojectors

We present a simple algorithm for constructing the N-extended superfield projection operators for irreducible representations of supersymmetry, and explicitly perform all simplifications due to spinor derivative algebra. The method is based on covariant expansion of a general superfield in terms of chiral superfields, and requires no knowledge of Casimir operators. We list these superprojectors for various N = 1, 2, and 4 superfields, and apply our results to quantized the linearized N = 2 vector multiplet in a supersymmetric gauge.     

One-loop effective action in three-dimensional general chiral superfield model

Using the heat kernel approach we calculate one-loop Kähler effective potential for the general chiral superfield model in three dimensions.     

Deformation of Curved BPS Domain Walls and Supersymmetric Flows on 2<Emphasis Type="Italic">d</Emphasis> Kähler-Ricci Soliton

We consider some aspects of the curved BPS domain walls and their supersymmetric Lorentz invariant vacua of the four dimensional N = 1 supergravity coupled to a chiral multiplet. In particular, the scalar manifold can be viewed as a two dimensional Kähler-Ricci soliton generating a one-parameter family of Kähler manifolds evolved with respect to a real parameter, τ. This implies that all quantities describing the walls and their vacua indeed evolve with respect to τ. Then, the analysis on the eigenvalues of the first order expansion of BPS equations shows that in general the vacua related to the field theory on a curved background do not always exist. In order to verify their existence in the ultraviolet or infrared regions one has to perform the renormalization group analysis. Finally, we discuss in detail a simple model with a linear superpotential and the Kähler-Ricci soliton considered as the Rosenau solution.     

Obstructions to the Existence of Sasaki–Einstein Metrics

We describe two simple obstructions to the existence of Ricci-flat Kähler cone metrics on isolated Gorenstein singularities or, equivalently, to the existence of Sasaki-Einstein metrics on the links of these singularities. In particular, this also leads to new obstructions for Kähler–Einstein metrics on Fano orbifolds. We present several families of hypersurface singularities that are obstructed, including 3-fold and 4-fold singularities of ADE type that have been studied previously in the physics literature. We show that the AdS/CFT dual of one obstruction is that the R–charge of a gauge invariant chiral primary operator violates the unitarity bound.     

Supersymmetric nonlinear sigma model in AdS5

We construct the supersymmetric nonlinear sigma model in a fixed AdS₅ background. We use component fields and find that the complex bosons must be the coordinates of a hyper-Kähler manifold that admits a Killing vector satisfying an inhomogeneous tri-holomorphic condition. We propose boundary conditions that map the on-shell bulk hypermultiplets into off-shell chiral multiplets on 3-branes that foliate the bulk. The supersymmetric AdS₅ isometries reduce to superconformal transformations on the brane fields.     

N = 4 Yang-Mills theory on the light cone

The 10-dimensional supersymmetric Yang-Mills theory is constructed in the light-cone gauge. When the theory is dimensionally reduced to four dimensions it is shown that the corresponding N = 4 theory is conveniently described in terms of a scalar superfield. This formalism avoids the problem of auxiliary fields but is Lorentz invariant only on the mass shell. Similar formalisms in terms of scalar superfields are also sketched for the other supersymmetric Yang-Mills as well as for N = 8 supergravity.     

Improved methods for supergraphs

We introduce some new techniques into superfield perturbation theory which allow considerable simplifications in calculations. As a result, we show that all contributions to the effective action can be written as integrals over a single d⁴θ. We also give the background group field formalism for supersymmetric non-abelian gauge theories. To illustrate our methods, we give examples of loop calculations: in particular, we show that in O(4) extended supersymmetric non-abelian gauge theories all one-loop propagator corrections cancel identically (both infinite and finite parts) and that these theories, at one loop, are finite and have no renormalizations (in the Fermi-Feynman gauge).     

The background field method and the ultraviolet structure of the supersymmetric nonlinear σ-model

Calculations of the ultraviolet counterterms of the bosonic and supersymmetric nonlinear σ-models in two space-time dimensions are undertaken in order to verify conclusions of a recent argument based on differential geometry in the supersymmetric case. The background field method and the normal coordinate expansion are discussed in detail, and the generalized renormalization group pole equations applicable to the nonlinear σ-model are derived. Both component and superfield calculations of the counterterms are presented.     

Supersymmetry and central charges

Superfield representations of supersymmetry algebras with central charges are studied. An interacting field theory realization of the SU(2) invariant example is given, which is shown to be just another interpretation of P. Fayet's “hypersymmetry”. For certain massless cases it is shown that the theory has a larger SU(4) invariance once the equations of motion are used, thus providing us with a possible superfield formulation of the SU(4) supersymmetric gauge theory.     

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.     

N = 1 superspace formulation of N = 2 and N = 4 super-Yang-Mills models with central charge

The component models of N = 2 and N = 4 supersymmetric Yang-Mills theories of Sohnius, Stelle and West are reformulated in terms of N = 1 superfields. The non-supersymmetric constraints are supersymmetrized generalizing the linear multiplet in the presence of the non-abelian gauge superfield and (in the N = 4 case) a doublet of chiral superfields. The extended supersymmetry transformations preserving constraints are explicitly given in terms of N = 1 superfields. We are able to introduce the constraints back into the lagrangian using superfield Lagrange multipliers. The on-shell equivalence of this formulation with the formulation of Fayet with one (for N = 2) and three (for N = 4) chiral superfields is shown. The abelian N = 2 model is worked out to show the connection between full superspace treatment and the N = 1 superfield formulation.     

Natural μ and Bμ in gauge mediation

We propose a natural solution to the μ problem in gauge mediation. It relies on the logarithmic dependence of the effective Kähler potential on the messenger threshold superfield X. Thus, μ and Bμ naturally arise at one and two loops, respectively. Moreover B has the same phase as the gaugino mass and the supersymmetric CP problem is solved as well.     

Realistic Type IIB supersymmetric Minkowski flux vacua

We show that there exist supersymmetric Minkowski vacua on Type IIB toroidal orientifold with general flux compactifications where the RR tadpole cancellation conditions can be relaxed elegantly. Then we present a realistic Pati–Salam like model. At the string scale, the gauge symmetry can be broken down to the Standard Model (SM) gauge symmetry, the gauge coupling unification can be achieved naturally, and all the extra chiral exotic particles can be decoupled so that we have the supersymmetric SMs with/without SM singlet(s) below the string scale. The observed SM fermion masses and mixings can also be obtained. In addition, the unified gauge coupling, the dilaton, the complex structure moduli, the real parts of the Kähler moduli and the sum of the imaginary parts of the Kähler moduli can be determined as functions of the four-dimensional dilaton and fluxes, and can be estimated as well.