We analyze several aspects of R-symmetry and supersymmetry breaking in generalized O'Raifeartaigh models with non-canonical Kahler potential. Some conditions on the Kahler potential are derived in order for the non-supersymmetric vacua to be degenerate. We calculate the Coleman-Weinberg (CW) effective potential for general quiral non-linear sigma models and then study the 1-loop quantum corrections to the pseudo-moduli space. For R-symmetric models, the quadratic dependence of the CW potential with the ultraviolet cutoff scale disappears. We also show that the conditions for R-symmetry breaking are independent of this scale and remain unchanged with respect to those of canonical models. This is, R-symmetry can be broken when generic R-charge assignments to the fields are made, while it remains unbroken when only fields with R-charge 0 and 2 are present. We further show that these models can keep the runaway behavior of their canonical counterparts and also new runaway directions can be induced. Due to the runaway directions, the non-supersymmetric vacua is metastable.
We analyse with the algebraic, regularisation independent, cohomological B.R.S. methods, the renormalisability of torsionless N=2 supersymmetric non-linear $\si$ models built on compact Kähler spaces. Surprisingly enough with respect to the common wisdom, we obtain an anomaly candidate, when the Hodge number $h^{3,0}$ of the target space manifold is different from zero : this occurs in particular in the Calabi-Yau case. On the contrary, in the compact homogeneous Kähler case, the anomaly candidate disappears.
We investigate a 2-dimensional N=2 supersymmetric model which consists of n chiral superfields with Kahler potential. When we define quantum observables, we are always plagued by operator ordering problem. Among various ways to fix the operator order, we rely upon the supersymmetry. We demonstrate that the correct operator order is given by requiring the super Poincare algebra by carrying out the canonical Dirac bracket quantization. This is shown to be also true when the supersymmetry algebra has a central extension by the presence of topological soliton. It is also shown that the path of sol…
We use a new mechanism for generating a Fayet-Iliopoulos term in supergravity, which is not associated to an R symmetry, to construct a semi-realistic theory of slow-roll inflation for a theory with the same Kähler potential and superpotential as the KKLT string background (without anti-D3 branes). In our model, supersymmetry must be broken at a high scale in a hidden sector to ensure that the cutoff of the effective field theory is above the Hubble scale of inflation. The gravitino has a super-EeV mass and supersymmetry breaking is communicated to the observable sector through gravity mediati…
We propose an alternative for the Clebsch decomposition of currents in fluid mechanics, in terms of complex potentials taking values in a Kahler manifold. We reformulate classical relativistic fluid mechanics in terms of these complex potentials and rederive the existence of an infinite set of conserved currents. We perform a canonical analysis to find the explicit form of the algebra of conserved charges. The Kahler-space formulation of the theory has a natural supersymmetric extension in 4-D space-time. It contains a conserved current, but also a number of additional fields complicating the …
Field redefinitions at string 1-loop order are often required by supersymmetry, for instance in order to make the Kähler structure of the scalar kinetic terms manifest. We derive the general structure of the field redefinitions and the Kähler potential at string 1-loop order in a certain class of string theory models (4-dimensional toroidal type IIB orientifolds with ${\cal N}=1$ supersymmetry) and for a certain subsector of fields (untwisted Kähler moduli and the 4-dimensional dilaton). To do so we make use of supersymmetry, perturbative axionic shift symmetries and a particular ansatz for th…
We solve the long standing problem of finding an off-shell supersymmetric formulation for a general N = (2, 2) nonlinear two dimensional sigma model. Geometrically the problem is equivalent to proving the existence of special coordinates; these correspond to particular superfields that allow for a superspace description. We construct and explain the geometric significance of the generalized Kahler potential for any generalized Kahler manifold; this potential is the superspace Lagrangian.
We construct two new versions of the c-map which allow us to obtain the target manifolds of hypermultiplets in Euclidean theories with rigid N =2 supersymmetry. While the Minkowskian para-c-map is obtained by dimensional reduction of the Minkowskian vector multiplet lagrangian over time, the Euclidean para-c-map corresponds to the dimensional reduction of the Euclidean vector multiplet lagrangian. In both cases the resulting hypermultiplet target spaces are para-hyper-Kahler manifolds. We review and prove the relevant results of para-complex and para-hypercomplex geometry. In particular, we gi…
We determine one-loop string corrections to Kahler potentials in type IIB orientifold compactifications with either N=1 or N=2 supersymmetry, including D-brane moduli, by evaluating string scattering amplitudes.
We consider supergravity solutions corresponding to D7 branes wrapped on Kahler manifolds with a U(1)_R twist such that some supersymmetry is preserved. We find a class of 1/4-BPS backgrounds where a D7-brane is wrapped on a T^2 torus with a metric of non-constant curvature. Similarly to the flat D7-brane case, the solution has a singularity at finite radius. We also discuss the case where the D7-brane is wrapped on a 4-dimensional non-compact manifold. The field theories on the D7 brane have N=1 supersymmetry in 6 and 4 dimensions respectively.
The known supergravity solution for wrapped D5-branes on the two-cycle of a Kahler resolved conifold is in general ISD but not supersymmetric, with the supersymmetry being broken by the presence of (1, 2) fluxes. However if we allow a non-Kahler metric on the resolved conifold, supersymmetry can easily be restored. The vanishing of the (1, 2) fluxes here corresponds to, under certain conformal rescalings of the metric, the torsion class constraints. We construct a class of explicit non-Kahler metrics on the resolved conifold satisfying the constraints. All this can also be studied from M-theor…
We show that contrary to the common lore it is possible to spontaneously break N=2 supersymmetry even in simple theories without constant Fayet-Iliopoulos terms. We consider the most general N=2 supersymmetric theory with one hypermultiplet and one vector multiplet without Fayet-Iliopoulos terms, and show that metastable supersymmetry breaking vacua can arise if both the hyper-Kahler and the special-Kahler geometries are suitably curved. We then also prove that while all the scalars can be massive, the lightest one is always lighter than the vector boson. Finally, we argue that these results a…
We discuss the conditions for additional supersymmetry and twisted supersymmetry in N = (2, 2) supersymmetric non-linear sigma models described by one left and one right semi-chiral superfield and carrying a pair of non-commuting complex structures. Focus is on linear non-manifest transformations of these fields that have an algebra that closes off-shell. We find that additional linear supersymmetry has no interesting solution, whereas additional linear twisted supersymmetry has solutions with interesting geometrical properties. We solve the conditions for invariance of the action and show tha…
A new mechanism of supersymmetry breaking involving a dynamical parameter is introduced. It is independent of particle phenomenology and gauge groups. An explicit realization of this mechanism takes place in Type II superstring compactifications which admit eight supercharges (also known as generalized SU(3) structures). The resulting Kahler potentials are expressed in terms of Hitchin functionals.
We study topological gauge theories with N=(2,0) supersymmetry based on stable bundles on general Kahler 3-folds. In order to have a theory that is well defined and well behaved, we consider a model based on an extension of the usual holomorphic bundle by including a holomorphic 3-form. The correlation functions of the model describe complex 3-dimensional generalizations of Donaldson-Witten type invariants. We show that the path integral can be written as a sum of contributions from stable bundles and a complex 3-dimensional version of Seiberg-Witten monopoles. We study certain deformations of…
Gravity duals for a class of UV complete minimally supersymmetric non-conformal gauge theories require deformed conifolds with fluxes. However these manifolds do not allow for the standard Kahler or conformally Kahler metrics on them, instead the metrics are fully non-Kahler. We take a generic such configuration of a non-Kahler deformed conifold with fluxes and ask what constraints do supersymmetry impose in the Baryonic branch. We study the supersymmetry conditions and show that for the correct choices of the vielbeins and the complex structure all the equations may be consistently solved. Th…
We investigate the generalized gauge theory which has been proposed previously and show that in two dimensions the instanton gauge fixing of the generalized topological Yang-Mills action leads to a twisted N=2 supersymmetric action. We have found that the R-symmetry of N=2 supersymmetry can be identified with the flavour symmetry of Dirac-Kahler fermion formulation. Thus the procedure of twist allows topological ghost fields to be interpreted as the Dirac-Kahler matter fermions.
Supersymmetric SU(N_C) gauge theories possess runaway-type superpotentials for N_F < N_C, where N_F is the flavor number of massless quarks. We show that the runaway behavior can be stabilized for N_F nearly equal to N_C by introducing singlets with the aid of perturbative corrections to the Kahler potential, generating (local) minima of supersymmetry breaking.
We show that the usual dilaton dominance scenario, derived from the tree level Kähler potential, can never correspond to a global minimum of the potential at $V=0$. Similarly, it cannot correspond to a local minimum either, unless a really big conspiracy of different contributions to the superpotential $W(S)$ takes place. These results, plus the fact that the Kähler potential is likely to receive sizeable string non-perturbative contributions, strongly suggest to consider a more general scenario, leaving the Kähler potential arbitrary. In this way we obtain generalized expressions for the soft…
We study the influence of anomalous U(1) symmetries and their associated D-terms on the vacuum structure of global field theories once they are coupled to N=1 supergravity and in the context of string compactifications with moduli stabilisation. In particular, we focus on a IIB string motivated construction of the ISS scenario and examine the influence of one additional U(1) symmetry on the vacuum structure. We point out that in the simplest one-Kahler modulus compactification, the original ISS vacuum gets generically destabilised by a runaway behaviour of the potential in the modulus directio…
New heterotic torsional geometries are constructed as orbifolds of T^2 bundles over K3. The discrete symmetries considered can be freely-acting or have fixed points and/or fixed curves. We give explicit constructions when the base K3 is Kummer or algebraic. The orbifold geometries can preserve N=1,2 supersymmetry in four dimensions or be non-supersymmetric.
The partition function of four-dimensional N=2 superconformal field theories on S^4 computes the exact Kahler potential on the space of exactly marginal couplings [1]. We present a new elementary proof of this result using supersymmetry Ward identities. The partition function is a section rather than a function, and is subject to ambiguities coming from Kahler transformations acting on the Kahler potential. This ambiguity is realized by a local supergravity counterterm in the underlying SCFT. We provide an explicit construction of the Kahler ambiguity counterterm in the four dimensional N=2 of…
We analyse with the algebraic, regularisation independant, cohomological B.R.S. methods, the renormalisability of torsionless N=2 and N= 4 supersymmetric non-linear $\si$ models built on Kähler spaces. Surprisingly enough with respect to the common wisdom, in the case of N=2 supersymmetry, we obtain an anomaly candidate, at least in the compact Kähler Ricci-flat case. If its coefficient does differ from zero, such anomaly would imply the breaking of global N=2 supersymmetry and get into trouble some schemes of superstring compactification as such non-linear $\si$ models offer candidates for th…
Supersymmetry of the Wess-Zumino (N=1, D=4) multiplet allows field equations that determine a larger class of geometries than the familiar Kahler manifolds, in which covariantly holomorphic vectors rather than a scalar superpotential determine the forces. Indeed, relaxing the requirement that the field equations be derivable from an action leads to complex flat geometry. The Batalin-Vilkovisky formalism is used to show that if one requires that the field equations be derivable from an action, we once again recover the restriction to Kahler geometry, with forces derived from a scalar superpoten…
We examine the conditions for superconformal invariance and the specific form of the Kähler potential for a two-dimensional lagrangian model with $N=2$ supersymmetry and superpotential $gX^k$. Away from the superconformal point we study the renormalization group flow induced by a particular class of Kähler potentials. We find trajectories which, in the infrared, reach the fixed point with a central charge whose value is that of the $N=2$, $A_{k-1}$ minimal model.
We study the origin of fermion mass hierarchy and flavor mixing in the standard model, paying attention to flavor symmetries and fermion kinetic terms. There is a possibility that the hierarchical flavor structure of quarks and charged leptons originates from non-canonical types of fermion kinetic terms in the presence of flavor symmetric Yukawa interactions. A flavor symmetry can be hidden in the form of non-unitary bases in the standard model. The structure of Kähler potential can become a touchstone of new physics.
The statistics of the supersymmetry breaking scale in the string landscape has been extensively studied in the past finding either a power-law behaviour induced by uniform distributions of F-terms or a logarithmic distribution motivated by dynamical supersymmetry breaking. These studies focused mainly on type IIB flux compactifications but did not systematically incorporate the Kähler moduli. In this paper we point out that the inclusion of the Kähler moduli is crucial to understand the distribution of the supersymmetry breaking scale in the landscape since in general one obtains unstable vacu…
We study a broad class of two dimensional gauged linear sigma models (GLSMs) with off-shell N=(2,2) supersymmetry that flow to nonlinear sigma models (NLSMs) on noncompact geometries with torsion. These models arise from coupling chiral, twisted chiral, and semichiral multiplets to known as well as to a new N=(2,2) vector multiplet, the constrained semichiral vector multiplet (CSVM). We discuss three kinds of models, corresponding to torsionful deformations of standard GLSMs realizing Kahler, hyperkahler, and Calabi-Yau manifolds. The (2,2) supersymmetry guarantees that these spaces are genera…
We derive the supersymmetric low-energy effective theory of the D-flat directions of a supersymmetric gauge theory. The Kahler potential of Affleck, Dine and Seiberg is derived by applying holomorphic constraints which manifestly maintain supersymmetry. We also present a simple procedure for calculating all derivatives of the Kahler potential at points on the flat direction manifold. Together with knowledge of the superpotential, these are sufficient for a complete determination of the spectrum and the interactions of the light degrees of freedom. We illustrate the method on the example of a c…
We give an intrinsic definition of the special geometry which arises in global N=2 supersymmetry in four dimensions. The base of an algebraic integrable system exhibits this geometry, and with an integrality hypothesis any special Kahler manifold is so related to an integrable system. The cotangent bundle of a special Kahler manifold carries a hyperkahler metric. We also define special geometry in supergravity in terms of the special geometry in global supersymmetry.
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 discuss a new interaction for chiral models in four-dimensional ${\cal N}=1$ supergavity. It contains a new arbitrary function in addition to the Kähler potential and superpotential. Its features include linearly realized off-shell supersymmetry, Kähler-Weyl invariance and broken supersymmetry. The corresponding scalar potential is augmented by the arbitrary function which allows freedom in constructing low-energy phenomenological models and inflationary models rooted in supergravity.
We consider Dynamical Supersymmetry Breaking (DSB) in models with classical flat directions. We analyze a number of examples, and develop a systematic approach to determine if classical flat directions are stabilized in the full quantum theory, or lead to run-away behavior. In some cases pseudo-flat directions remain even at the quantum level before taking into account corrections to the Kähler potential. We show that in certain limits these corrections are calculable. In particular, we find that in the Intriligator-Thomas $SU(2)$ and its generalizations, a potential for moduli is generated. M…
Using the flux compactification scenario in a generic supergravity model we construct a set of conditions which are necessary to generate de-Sitter or anti de-Sitter vacua for appropriate choices of the parameters in superpotential. It is shown that a mass spectrum consistent with softly broken TeV scale supersymmetry in a minimal supersymmetric standard model at the observable sector can be obtained along with a tiny cosmological constant when the Kahler and superpotential of the hidden sector satisfy a set of general constraints. Constructing a specific model with Kahler and superpotentials …
We present explicit constructions of complete Ricci-flat Kahler metrics that are asymptotic to cones over non-regular Sasaki-Einstein manifolds. The metrics are constructed from a complete Kahler-Einstein manifold (V,g_V) of positive Ricci curvature and admit a Hamiltonian two-form of order two. We obtain Ricci-flat Kahler metrics on the total spaces of (i) holomorphic C^2/Z_p orbifold fibrations over V, (ii) holomorphic orbifold fibrations over weighted projective spaces WCP^1, with generic fibres being the canonical complex cone over V, and (iii) the canonical orbifold line bundle over a fam…
We show that the anomaly-mediated supersymmetry breaking via the Kahler and sigma-model anomalies is suppressed by conformal dynamics in the supersymmetry breaking sector.
We consider a general d=4 N=1 globally supersymmetric lagrangian involving chiral and vector superfields, with arbitrary superpotential, Kahler potential and gauge kinetic function. We compute perturbative quantum corrections by employing a component field approach that respects supersymmetry and background gauge invariance. In particular, we obtain the full one-loop correction to the Kahler potential in supersymmetric Landau gauge. Two derivations of this result are described. The non-renormalization of the superpotential and the quadratic correction to the Fayet-Iliopoulos terms are further …
We carry out a model-independent EFT method study on the vacuum statistics of general F-term SUSY breaking models. Assuming a smooth distribution of Lagrangian parameters, SUSY breaking vacua are rare in global SUSY models with a canonical Kähler potential, and have a peaked distribution near the cut-off of the SUSY breaking scale in both global SUSY and SUGRA models with a general Kähler potential. After including different mass scales in the Lagrangian, we compare the total number of SUSY and non-SUSY vacua and estimate quantitatively the rareness of SUSY breaking. The EFT method provides a …
In global supersymmetric Wess-Zumino models with minimal Kähler potentials, F-type supersymmetry breaking always yields instability or continuous degeneracy of non-supersymmetric vacua. As a generalization of the original O'Raifeartaigh's result, the existence of instability or degeneracy is true to any higher order corrections at tree level for models even with non-renormalizable superpotentials. The degeneracy generically coincides the R-axion direction under some assumptions of R-charge assignment, but generally requires neither R-symmetries nor any assumption of generic superpotentials. Th…
We study reheating after the end of inflation in models where the inflaton is the superpartner of goldstino and is charged under a gauged $U(1)$ R-symmetry. We consider two classes of models -- one is small field characterized by an almost flat Kähler space, and the other large field characterized by a hyperbolic Kähler space $SU(1,1)/U(1)$, while in both cases the inflaton superpotential is linear due to the R-symmetry. The inflationary observables of our models fit within 2$σ$ CMB values. Upon coupling the inflaton sector to the (supersymmetric) Standard Model, we compute the MSSM parameters…
We review the effects of heavy scalar fields during inflation in the framework of $\mathcal N = 1$ supergravity. Such heavy scalars can be geometric moduli from string compactifications or stabilizer fields from a different sector of the theory. Even when these fields are heavier than the Hubble scale during inflation, they generically cause backreactions which alter the dynamics of the system. Severe problems may arise when the heavy fields break supersymmetry, which is quite generic for Kähler moduli. We illustrate these effects in two examples, chaotic inflation and Starobinsky-like inflati…
A coset model based on the hyperbolic Kac-Moody algebra E10 has been conjectured to underly eleven-dimensional supergravity and M theory. In this note we study the canonical structure of the bosonic model for finite- and infinite-dimensional groups. In the case of finite-dimensional groups like GL(n) we exhibit a convenient set of variables with Borel-type canonical brackets. The generalisation to the Kac-Moody case requires a proper treatment of the imaginary roots that remains elusive. As a second result, we show that the supersymmetry constraint of D=11 supergravity can be rewritten in a su…
Supersymmetry breaking via gaugino condensation is studied in vacua of heterotic M-theory with five-branes. We show that supersymmetry is still broken by a global mechanism and that the non-perturbative superpotential takes the standard form. When expressed in terms of low energy fields, a modification arises due to a threshold correction in the gauge kinetic function that depends on five-brane moduli. We also determine the form of the low energy matter field Kahler potential. These results are used to discuss the soft supersymmetry breaking parameters, in particular the question of universali…
We show how to lift solutions of Euclidean Einstein-Maxwell equations with non-zero cosmological constant to solutions of eleven-dimensional supergravity theory with non-zero fluxes. This yields a class of 11D metrics given in terms of solutions to $SU(\infty)$ Toda equation. We give one example of a regular solution and analyse its supersymmetry. We also analyse the integrability conditions of the Killing spinor equations of N=2 minimal gauged supergravity in four Euclidean dimensions. We obtain necessary conditions for the existence of additional Killing spinors, corresponding to enhancement…
We revisit the backgrounds of type IIB on manifolds with $SU(4)$-structure and discuss two sets of solutions arising from internal geometries that are complex and symplectic respectively. Both can be realized in terms of generalized complex geometry. We identify a map which relates the complex and symplectic supersymmetric systems. In the semi-flat torus bundle setting this map corresponds to T-duality and suggest a way of extending the mirror transform to non-Kähler geometries.
The string landscape suggests that the supersymmetry breaking scale can be high, and then the simplest low energy effective theory is the Standard Model (SM). Considering grand unification scale supersymmetry breaking, we show that gauge coupling unification can be achieved at about 10^{16-17} GeV in the SM with suitable normalizations of the U(1)_Y, and we predict that the Higgs mass range is 127 GeV to 165 GeV, with the precise value strongly correlated with the top quark mass m_t and SU(3)_C gauge coupling. For example, if m_t=178\pm1 GeV, the Higgs boson mass is predicted to be between 141…
We assess which Kahler potentials in supergravity lead to viable single-field inflationary models that are consistent with Planck. We highlight the role of symmetries, such as shift, Heisenberg and supersymmetry, in these constructions. Also the connections to string theory are pointed out. Finally, we discuss a supergravity model for arbitrary inflationary potentials that is suitable for open string inflation and generalize it to the case of closed string inflation. Our model includes the recently discussed supergravity reformulation of the Starobinsky model of inflation as well as an interes…
