Within a superfield approach, we formulate a simple quantum generating equation of the field - antifield formalism. Then, we derive the Schroedinger equation with the Hamiltonian whose $Δ$ - exact part serves as a generator to the quantum master-transformations. We show that these generators do satisfy a nice composition law in terms of the quantum antibrackets. We also present an $Sp(2)$ symmetric extension as to the main construction, with specific features caused with the principal fact that all basic equations become $Sp(2)$ vector valued ones.
A simple quantum superfield generating equation of the field-antifield formalism is proposed. The Schroedinger equation with the Hamiltonian having $Δ$-exact form is derived. An $Sp(2)$ symmetric extension to the main construction, with specific features caused by the principal fact that all basic equations become $Sp(2)$ vector-valued ones, is presented. A principal role of quantum antibrackets in formulation of the Heisenberg equations of motion is shown.
We propose a superfield formalism of Lagrangian BRST-antiBRST quantization of arbitrary gauge theories in general coordinates with the base manifold of fields and antifields desribed in terms of both bosonic and fermionic variables.
The multilevel field-antifield formalism is constructed in a geometrically covariant way without imposing the unimodularity conditions on the hypergauge functions. Thus the previously given version [1,2] is extended to cover the most general case of Lagrangian surface bases. It is shown that the extra measure factors, required to enter the gauge-independent functional integrals, can be included naturally into the multilevel scheme by modifying the boundary conditions to the quantum master equation.
A general quantum-mechanical setting is proposed for the field-antifield formalism as a unique hyper-gauge theory in the field-antifield space. We formulate a Schrödinger-type equation to describe the quantum evolution in a "current time" purely formal in its nature. The corresponding Hamiltonian is defined in the form of a supercommutator of the delta-operator with a hyper-gauge Fermion. The initial wave function is restricted to be annihilated with the delta-operator. The Schrödinger's equation is resolved in a closed form of the path integral, whose action contains the symmetric Weyl's symb…
A generalized version is proposed for the field-antifield formalism. The antibracket operation is defined in arbitrary field-antifield coordinates. The antisymplectic definitions are given for first- and second-class constraints. In the case of second-class constraints the Dirac's antibracket operation is defined. The quantum master equation as well as the hypergauge fixing procedure are formulated in a coordinate-invariant way. The general hypergauge functions are shown to be antisymplectic first-class constraints whose Jacobian matrix determinant is constant on the constraint surface. The BR…
A Batalin-Vilkovisky action for D=6, N=1 super-Yang--Mills theory, including coupling to hypermultiplets, is given. The formalism involves pure spinor superfields. The geometric properties of the D=6, N=1 pure spinors (which differ from Cartan pure spinors) are examined. Unlike the situation for maximally supersymmetric models, the fields and antifields (including ghosts) of the vector multiplet reside in separate superfields. The formalism provides an off-shell superspace formulation for matter hypermultiplets, which in a traditional treatment are on-shell.
The multilevel geometrically--covariant generalization of the field--antifield BV--formalism is suggested. The structure of quantum generating equations and hypergauge conditions is studied in details. The multilevel formalism is established to be physically--equivalent to the standard BV--version.
We construct a Wilson action for the Wess-Zumino model by applying the exact renormalization group perturbatively. Using neither superfields nor auxiliary fields, we construct a supersymmetric action only with complex scalar and Majorana spinor fields. We adopt the BRST (antifield) formalism to show the consistency of the construction to all orders in loop expansions. The resulting action has a quadratically divergent scalar mass term which is absent in the superfield formalism.
It is shown that the quantum master equation of the Field Antifield quantization method at one loop order can be translated into the requirement of a superfield structure for the action. The Pauli Villars regularization is implemented in this BRST superspace and the case of anomalous gauge theories is investigated. The quantum action, including Wess Zumino terms, shows up as one of the components of a superfield that includes the BRST anomalies in the other component. The example of W2 quantum gravity is also discussed.
It has recently been shown that the Field Antifield quantization of anomalous irreducible gauge theories with closed algebra can be represented in a BRST superspace where the quantum action at one loop order, including the Wess Zumino term, and the anomalies show up as components of the same superfield. We show here how the Chiral Schwinger model can be represented in this formulation.
The rules of local superfield Lagrangian quantization in reducible non-Abelian hypergauge functions are formulated for an arbitrary gauge theory. The generating functionals of standard and vertex Green's functions which depend on the Grassmann variable $η$ via super(anti)fields and sources are constructed. The difference between the local quantum and the gauge fixing actions determines an almost Hamiltonian system such that translations with respect to $η$ along the solutions of this system define the superfield BRST transformations. The Ward identities are derived and the gauge independence o…
In this paper, we study the third quantized super-group field cosmology, a model in multiverse scenario, in Batalin-Vilkovisky (BV) formulation. Further, we propose the superfield/super-antifield dependent BRST symmetry transformations. Within this formulation, we establish connection between the two different solutions of the quantum master equation within the BV formulation.
We study the structure of holomorphic effective action for hypermultiplet models interacting with background super Yang-Mills fields. A general form of holomorphic effective action is found for hypermultiplet belonging to arbitrary representation of any semisimple compact Lie group spontaneously broken to its maximal abelian subgroup. The applications of obtained results to hypermultiplets in fundamental and adjoint representations of the SU(n), SO(n), Sp(n) groups are considered.
Unconstrained ${\cal N}=2$ higher-spin gauge superfields and their hypermultiplet couplings
Tomsk State Pedagogical University（托木斯克国立师范学院）；Bogoliubov Laboratory of Theoretical Physics, JINR（约飞联合核子研究所波哥留博夫理论物理实验室）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）
We construct manifestly $4D, \mathcal{N}=2$ supersymmetric and gauge invariant off-shell cubic couplings of matter hypermultiplets to the higher integer spin gauge $\mathcal{N}=2$ multiplets introduced in arXiv:2109.07639 [hep-th]. The hypermultiplet is described by an analytic harmonic $4D, \mathcal{N}=2$ superfield $q^{+}$ with the physical component spins ${\bf s} = (\frac{1}{2}\,, \;0)$ and an infinite number of auxiliary fields. The cubic coupling constructed has the schematic structure $q^+ \hat{\cal H}^{++}_{(s)} q^+$, where $\hat{\cal H}^{++}_{(s)}$ is a differential analytic operator …
We construct an action for holomorphic Chern-Simons theory that couples the gauge field to off-shell gravitational backgrounds, comprising the complex structure and the (3,0)-form of the target space. Gauge invariance of the off-shell action is achieved by enlarging the field space to include an appropriate system of Lagrange multipliers, ghost and ghost-for-ghost fields. Both the BRST transformations and the BV action are compactly and neatly written in terms of superfields which include fields, backgrounds and their antifields. We show that the anti-holomorphic target space derivative can be…
We extend the results of arXiv:1401.1645 on the generalized conformal Sp(2n)-structure of infinite multiplets of higher spin fields, formulated in spaces with extra tensorial directions (hyperspaces), to the description of OSp(1|2n)-invariant infinite-dimensional higher-spin supermultiplets formulated in terms of scalar superfields on flat hyper-superspaces and on OSp(1|n) supergroup manifolds. We find generalized superconformal transformations relating the superfields and their equations of motion in flat hyper-superspace with those on the OSp(1|n) supermanifold. We then use these transformat…
We consider the six dimensional hypermultiplet, vector and tensor multiplet models in (1,0) harmonic superspace and discuss the corresponding superfield actions. The actions for free (2,0) tensor multiplet and for interacting vector/tensor multiplet system are constructed. Using the superfield formulation of the hypermultiplet coupled to the vector/tensor system we develop an approach to calculation of the one-loop superfield effective action and find its divergent structure.
We construct the classical action of the Aharony-Bergman-Jafferis-Maldacena (ABJM) model in the N=3, d=3 harmonic superspace. In such a formulation three out of six supersymmetries are realized off shell while the other three mix the superfields and close on shell. The superfield action involves two hypermultiplet superfields in the bifundamental representation of the gauge group and two Chern-Simons gauge superfields corresponding to the left and right gauge groups. The N=3 superconformal invariance allows only for a minimal gauge interaction of the hypermultiplets. Amazingly, the correct sex…
We study the quantum structure of four-dimensional ${\cal N}=2$ superfield sigma-model formulated in harmonic superspace in terms of the omega-hypermultiplet superfield $ω$. The model is described by harmonic superfield sigma-model metric $g_{ab}(ω)$ and two potential-like superfields $L^{++}_{a}(ω)$ and $L^{(+4)}(ω)$. In bosonic component sector this model describes some hyper-Kähler manifold. The manifestly ${\cal N}=2$ supersymmetric covariant background-quantum splitting is constructed and the superfield proper-time technique is developed to calculate the one-loop effective action. The one…
We propose an N=1 superfield formulation of Lagrangian quantization in general hypergauges by extending a reducible gauge theory to a superfield model with a local dependence on a Grassmann parameter $θ$. By means of $θ$-local functions of the quantum and gauge-fixing actions in terms of Darboux coordinates on the antisymplectic manifold, we construct superfield generating functionals of Green's functions, including the effective action. We prove the gauge-independence of the S-matrix, obtain the Ward identities and establish a relation of the proposed local quantization with the BV method and…
In this paper, by using the factorization equation of the ${\cal N}=2$ theory we study ${\cal N}=1$ supersymmetric SO(N) gauge theory in Argyres-Douglas points . We suppose that maximal confinement occurs in the system and give a tree level superpotential. Then, we obtain general Picard-fuchs equations for glueball superfield which are hypergeometric equations having regular singular points corresponding to Argyres-Douglas points. Furthermore, we study the solution of these differential equations and calculate the effective superpotential. Finally, we study scaling behavior of the chiral opera…
We illustrate the cosmological Friedmann-Robertson-Walker (FRW) models realized as gauge theory in the extended configuration space with its Becchi-Rouet-Stora-Tyutin (BRST) invariance upto total derivative. To investigate the model in Batalin-Vilkovisky (BV) formalism the Lagrangian density of the models is further extended by introducing shifted fields corresponding to all fields. The extended Lagrangian density having shifted fields admits more general BRST symmetry (including shift symmetry), called as extended BRST symmetry. In this framework the antighost fields corresponding to the shif…
We consider the six dimensional N=(1,0) hypermultiplet model coupled to an external field of the Abelian vector multiplet in harmonic superspace approach. Using the superfield proper-time technique we find the divergent part of the effective action and derive the complete finite induced low-energy superfield effective action. This effective action depends on external field and contains in bosonic sector all the powers of the constant Maxwell field strength. The obtained result can be treated as the 6D, N=(1,0) supersymmetric Heisenberg-Euler type effective action.
The mirror map in the D=3, N=4 supersymmetry connects the left and right SU(2) automorphism groups and also the superfield representations of the corresponding N=4 supermultiplets. The mirror N=4 harmonic superspaces use the harmonics of two SU(2) groups and two types of the Grassmann analyticity. The irreducible left and right N=4 supermultiplets are defined in these harmonic superspaces. We analyze the N=4 superconformal interactions of the gauge and matter superfields and the spontaneous breakdown of the superconformal symmetry. The most interesting superconformal action possesses the mirro…
We compute the one-loop holomorphic effective action of the massless Cartan sector of N=2 SYM theory in the Coulomb branch, taking into account the contributions both from the charged hypermultiplets and off-diagonal components of the gauge superfield. We use the manifestly supersymmetric harmonic superfields diagram techniques adapted to N=2 supersymmetry with the central charges induced by Cartan generators. The (anti)holomorphic part proves to be proportional to the central charges and it has the generic form of Seiberg's action obtained by integrating U(1) R-anomaly. It vanishes for N=4 SY…
We study the gauge dependence of the one-loop effective action for the abelian $6D$, ${\cal N}=(1,0)$ supersymmetric gauge theory formulated in harmonic superspace. We introduce the superfield $ξ$-gauge, construct the corresponding gauge superfield propagator, and calculate the one-loop two-and three-point Green functions with two external hypermultiplet legs. We demonstrate that in the general $ξ$-gauge the two-point Green function of the hypermultiplet is divergent, as opposed to the Feynman gauge $ξ=1$. The three-point Green function with two external hypermultiplet legs and one leg of the …
A $θ$-local formulation of superfield Lagrangian quantization in non-Abelian hypergauges is proposed on the basis of an extension of general reducible gauge theories to special superfield models with a Grassmann parameter $θ$. We solve the problem of describing the quantum action and the gauge algebra of an $L$-stage-reducible superfield model in terms of a BRST charge for a formal dynamical system with first-class constraints of $(L+1)$-stage reducibility. Starting from $θ$-local functions of the quantum and gauge-fixing actions, with an essential use of Darboux coordinates on the antisymplec…
We discuss the complete sets of the off-shell nilpotent (i.e. s^2_{(a)b} = 0) and absolutely anticommuting (i.e. s_b s_{ab} + s_{ab} s_b = 0) Becchi-Rouet-Stora-Tyutin (BRST) (s_b) and anti-BRST (s_{ab}) symmetries for the (3+1)-dimensional (4D) gauge-invariant massive 2-form theory within the framework of augmented superfield approach to BRST formalism. In this formalism, we obtain the coupled (but equivalent) Lagrangian densities which respect both BRST and anti-BRST symmetries on the constrained hypersurface defined by the Curci-Ferrari type conditions. The absolute anticommutativity proper…
We elaborate on the low-energy effective action of $6D,\,{\cal N}=(1,1)$ supersymmetric Yang-Mills (SYM) theory in the ${\cal N}=(1,0)$ harmonic superspace formulation. The theory is described in terms of analytic ${\cal N}=(1,0)$ gauge superfield $V^{++}$ and analytic $ω$-hypermultiplet, both in the adjoint representation of gauge group. The effective action is defined in the framework of the background superfield method ensuring the manifest gauge invariance along with manifest ${\cal N}=(1,0)$ supersymmetry. We calculate leading contribution to the one-loop effective action using the on-she…
We review the non-anticommutative Q-deformations of N=(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 preser…
We propose that the radion chiral supermultiplet of five dimensional compactified supergravity is obtained by reduction of the graviphoton gauge multiplet to N=1 superfields in the off shell 5D superconformal gravity formalism of Fujita, Kugo and Ohashi. We present a superfield Lagrangian of Chern-Simons type (similar to global SUSY), which reproduces all component couplings of gauge fields and the radion. A hypermultiplet superspace action is also proposed which correctly accounts for the coupling of matter multiplets with gauge and radion superfields. 4D supergravity enters by the coupling t…
In this paper we investigate three-dimensional superconformal gauge theories with N=3 supersymmetry. Independently from specific models, we derive the shortening conditions for unitary representations of the Osp(3|4) superalgebra and we express them in terms of differential constraints on three dimensional N=3 superfields. We find a ring structure underlying these short representations, which is just the direct generalization of the chiral ring structure of N=2 theories. When the superconformal field theory is realized on the world-volume of an M2-brane such superfield ring is the counterpart …
We present, in the N=2, D=4 harmonic superspace formalism, a general method for constructing the off-shell effective action of an N=2 abelian gauge superfield coupled to matter hypermultiplets. Using manifestly N=2 supersymmetric harmonic supergraph techniques, we calculate the low-energy corrections to the renormalized one-loop effective action in terms of N=2 (anti)chiral superfield strengths. For a harmonic gauge prepotential with vanishing vacuum expectation value, corresponding to massless hypermultiplets, the only non-trivial radiative corrections to appear are non-holomorphic. For a pre…
The requirements of N=1 superconformal invariance for the correlation functions of chiral superfields are analysed. Complete expressions are found for the three point function for the general spin case and for the four point function for scalar superfields for \sum q_i=3 where q_i is the scale dimension for the i'th superfield and is related to the U(1) R-charge. In the latter case the relevant Ward identities reduce to eight differential equations for four functions of u,v which are invariants when the superconformal symmetry is reduced to the usual conformal group. The differential equations…
We construct a new version of the higher covariant derivative regularization for a general ${\cal N}=2$ supersymmetric gauge theory formulated in terms of ${\cal N}=1$ superfields. This regularization preserves both supersymmetries of the classical action, namely, the invariance under the manifest ${\cal N}=1$ supersymmetry and under the second hidden on-shell supersymmetry. The regularizing ${\cal N}=2$ supersymmetric higher derivative term is found in the explicit form in terms of ${\cal N}=1$ superfields. Thus, ${\cal N}=2$ supersymmetry is broken only by the gauge fixing procedure. Then we…
We show that logarithmic conformal field theories may be derived using nilpotent scale transformation. Using such nilpotent weights we derive properties of LCFT's, such as two and three point correlation functions solely from symmetry arguments. Singular vectors and the Kac determinant may also be obtained using these nilpotent variables, hence the structure of the four point functions can also be derived. This leads to non homogeneous hypergeometric functions. Also we consider LCFT's near a boundary. Constructing "superfields" using a nilpotent variable, we show that the superfield of conform…
We continue studying $6D, {\cal N}=(1,1)$ supersymmetric Yang-Mills (SYM) theory in the ${\cal N}=(1,0)$ harmonic superspace formulation. Using the superfield background field method we explore the two-loop divergencies of the effective action in the gauge multiplet sector. It is explicitly demonstrated that among four two-loop background-field dependent supergraphs contributing to the effective action, only one diverges off shell. It is also shown that the divergences are proportional to the superfield classical equations of motion and hence vanish on shell. Besides, we have analyzed a possib…
We shortly review our new superfield formalism in the framework of Fujita, Kugo, Ohashi 5D conformal supergravity, in particular with an $S^1/Z_2$ orbifold. The radion of the fifth dimension is embedded in two related superfields, a chiral and a general multiplet and is linked to the radion superfield of rigid SUSY. The superspace action of the gauge sector is of the Chern-Simons type. We also present the superspace action for hypermultiplets and discuss the role of compensators. The presented formalism should be very useful for applications. We demonstrate this for obtaining the RS solution.
We discuss a formulation of harmonic superspace approach for noncommuative N=2 supersymmetric field theories paying main attention on new features arising because of noncommutativity. We begin with the known notions of the harmonic superfield models and results obtained and consider how these notions and results are modified in the noncommutative case. The actions of basic N=2 models, like hypermultiplet and N=2 vector multiplet, are given in terms of unconstrained off-shell superfields on noncommutative harmonic superspace. We calculate the low-energy contributions to the effective actions of…
We consider, in the harmonic superspace approach, the six-dimensional N=(1,0) supersymmetric model of abelian gauge multiplet coupled to a hypermultiplet. The superficial degree of divergence is evaluated and the structure of possible one-loop divergences is analyzed. Using the superfield proper-time and background-field technique, we compute the divergent part of the one-loop effective action depending on both the gauge multiplet and the hypermultiplet. The corresponding counterterms contain the purely gauge multiplet contribution together with the mixed contributions of the gauge multiplet a…
We provide a description of the five-dimensional Higgs mechanism in supersymmetric gauge theories compactified on the orbifold S^1/Z_2 by means of the N=1 superfield formalism. Goldstone bosons absorbed by vector multiplets can come either from hypermultiplets or from gauge multiplets of opposite parity (Hosotani mechanism). Supersymmetry is broken by the Scherk-Schwarz mechanism. In the presence of massive hypermultiplets and gauge multiplets, with different supersymmetric masses, the radion can be stabilized with positive (de Sitter) vacuum energy. The masses of vector and hypermultiplets ca…
The $\mathscr{N}=2^*$ supersymmetric gauge theory is a massive deformation of $\mathscr{N}=4$, in which the adjoint hypermultiplet gets a mass. We present a D-brane realisation of the (non-)Abelian $\mathscr{N}=2^*$ theory, and compute suitable topological amplitudes, which are expressed as a double series expansion. The coefficients determine couplings of higher-dimensional operators in the effective supergravity action that involve powers of the anti-self-dual $\mathscr{N}=2$ chiral Weyl superfield and of self-dual gauge field strengths superpartners of the D5-brane coupling modulus. In the …
The Higgs branch of N=2 supersymmetric gauge theories with non-Abelian gauge groups are described by hyper-Kahler (HK) nonlinear sigma models with potential terms. With the non-Abelian HK quotient by U(M) and SU(M) gauge groups, we give the massive HK sigma models that are not toric in the N=1 superfield formalism and the harmonic superspace formalism. The U(M) quotient gives N!/[M! (N-M)!] discrete vacua that may allow various types of domain walls, whereas the SU(M) quotient gives no discrete vacua.
BPS equations and wall solutions are studied keeping (part of) supersymmetry (SUSY) manifest. Using N=1 superfields, massive hyper-Kahler quotient is introduced to obtain massive N=2 (8 SUSY) nonlinear sigma models in four dimensions with T*CP(n) target manifold, which yield BPS wall solutions for the n=1 case. We also describe massive hyper-Kahler quotient of T*CP(n) by using the harmonic superspace formalism which preserves all SUSY manifestly, and BPS equations and wall solutions are obtained in the n=1 case.
We develop the formalism of "General gauge mediation" for five dimensional theories in a slice of AdS space. A set of current correlators encodes the effect of a supersymmetry breaking hidden sector localised on the IR brane. These current correlators provide a tree-level gaugino mass and loop-level sfermion masses on the UV brane. We also use this formalism to calculate the Casimir energy and masses for bulk hyperscalars. To illustrate this general construction we consider a perturbative hidden sector of generalised messengers coupled to a spurion. For models with large warping, we find that …
We use the "General Gauge Mediation" formalism to describe a 5D setup with an $S^{1}/Z_{2}$ orbifold. We first consider a model independent SUSY breaking hidden sector on one boundary and generic chiral matter on another. Using the definition of GGM, the effects of the hidden sector are contained in a set of global symmetry current correlator functions and is mediated through the bulk. We find the gaugino, sfermion and hyperscalar mass formulas for minimal and generalised messengers in different regimes of a large, small and intermediate extra dimension. Then we use the 5D GGM formalism to con…
