arXiv subjects
Publications and source records attributed to Zurab Kakushadze.
We discuss non-conformal non-supersymmetric large N gauge theories with vanishing vacuum energy density to all orders in perturbation theory. These gauge theories can be obtained via a field theory limit of Type IIB D3-branes embedded in orbifolded space-times. We also discuss gravity in this setup.
We discuss non-conformal gauge theories from type IIB D3-branes embedded in orbifolded space-times. Such theories can be obtained by allowing some non-vanishing logarithmic twisted tadpoles. In certain cases with N=0,1 supersymmetry correlation functions in the planar limit are the same as in the parent N=2 supersymmetric theories. In particular, the effective action in such theories perturbatively is not renormalized beyond one loop in the planar limit. In the N=2 as well as such N=0,1 theories quantum corrections in the D3-brane gauge theories are encoded in the corresponding classical higher dimensional field theories whose actions contain the twisted fields with non-vanishing tadpoles. We argue that this duality can be extended to the non-perturbative level in the N=2 theories. We give some evidence that this might also be the case for N=0,1 theories as well.
We construct a solitonic 3-brane solution in the 6-dimensional Einstein-Hilbert-Gauss-Bonnet theory with a (negative) cosmological term. This solitonic brane world is delta-function-like. Near the brane the metric is that for a product of the 4-dimensional flat Minkowski space with a 2-dimensional ``wedge'' with a deficit angle (which depends on the solitonic brane tension). Far from the brane the metric approaches that for a product of the 5-dimensional AdS space and a circle. This solitonic solution exists for a special value of the Gauss-Bonnet coupling (for which we also have a delta-function-like codimension-1 solitonic solution), and the solitonic brane tension can take values in a continuous range. We discuss various properties of this solitonic brane world, including coupling between gravity and matter localized on the brane.
Some time ago Dvali, Gabadadze and Senjanovic (hep-ph/9910207) discussed brane world scenarios with time-like extra dimensions. In this paper we construct a solitonic 3-brane solution in the 5-dimensional Einstein-Hilbert-Gauss-Bonnet theory with the space-time signature (-,+,+,+,-). The direction transverse to the brane is the second time-like direction. The solitonic brane is $δ$-function like, and has the property that gravity is completely localized on the brane. That is, there are no propagating degrees of freedom in the bulk, while on the brane we have purely 4-dimensional Einstein gravity. In particular, there are no propagating tachyonic or negative norm states even though the extra dimension is time-like.
We construct a solitonic 3-brane solution in the 5-dimensional Einstein-Hilbert-Gauss-Bonnet theory. This solitonic brane is delta-function like, and has the property that gravity is completely localized on the brane. That is, there are no propagating degrees of freedom in the bulk, while on the brane we have purely 4-dimensional Einstein gravity. Thus, albeit the classical background is 5-dimensional, the quantum theory (perturbatively) is 4-dimensional. Our solution can be embedded in the supergravity context, where we have completely localized supergravity on the corresponding solitonic brane, which is a BPS object preserving 1/2 of the original supersymmetries. By including a scalar field, we also construct a smooth domain wall solution, which in a certain limit reduces to the delta-function-like solitonic brane solution (this is possible for the latter breaks diffeomorphisms only spontaneously). We then show that in the smooth domain wall background the only normalizable mode is the 4-dimensional graviton zero mode, while all the other (including massive Kaluza-Klein) modes are not even plane-wave normalizable. Finally, we observe that in compactifications of Type IIB on 5-dimensional Einstein manifolds other than a 5-sphere the corresponding dual gauge theories on D3-branes are not conformal in the ultra-violet, and at the quantum level we expect the Einstein-Hilbert term to be generated in their world-volumes. We conjecture that in full string theory on Type IIB side this is due to higher curvature terms, which cannot be ignored in such backgrounds. A stronger version of this conjecture also states that (at least in some cases) in such backgrounds D3-branes are solitonic objects with completely localized (super)gravity in their world-volumes.
We discuss the gravitational Higgs mechanism in domain wall background solutions that arise in the theory of 5-dimensional Einstein-Hilbert gravity coupled to a scalar field with a non-trivial potential. The scalar fluctuations in such backgrounds can be completely gauged away, and so can be the graviphoton fluctuations. On the other hand, we show that the graviscalar fluctuations do not have normalizable modes. As to the 4-dimensional graviton fluctuations, in the case where the volume of the transverse dimension is finite the massive modes are plane-wave normalizable, while the zero mode is quadratically normalizable. We then discuss the coupling of domain wall gravity to localized 4-dimensional matter. In particular, we point out that this coupling is consistent only if the matter is conformal. This is different from the Randall-Sundrum case as there is a discontinuity in the delta-function-like limit of such a smooth domain wall - the latter breaks diffeomorphisms only spontaneously, while the Randall-Sundrum brane breaks diffeomorphisms explicitly. Finally, at the quantum level both the domain wall as well as the Randall-Sundrum setups suffer from inconsistencies in the coupling between gravity and localized matter, as well as the fact that gravity is generically expected to be delocalized in such backgrounds due to higher curvature terms.
We point out some subtleties with gauge fixings (which sometimes include the so-called ``brane bending'' effects) typically used to compute the graviton propagator on the Randall-Sundrum brane. In particular, the brane, which has non-vanishing tension, explicitly breaks some part of the diffeomorphisms, so that there are subtleties arising in going to, say, the axial gauge or the harmonic gauge in the presence of (non-conformal) matter localized on the brane. We therefore compute the graviton propagator in the gauge where only the graviphoton fluctuations are set to zero (the diffeomorphisms necessary for this gauge fixing are intact), but the graviscalar component is untouched. We point out that in the Gaussian normal coordinates (where the graviscalar component vanishes on the brane) the graviton propagator blows up in the ultra-violet near the brane. In fact, the allowed gauge transformations, which do not lead to such ultra-violet behavior of the graviton propagator, are such that the coupling of the graviscalar to the brane matter cannot be gauged away in the ultra-violet. Because of this, at the quantum level, where we expect various additional terms to be generated in the brane world-volume action including those involving the graviscalar, fine-tuning (which is independent of that for the brane cosmological constant) is generically required to preserve consistent coupling between bulk gravity and brane matter. We also reiterate that in such warped backgrounds higher curvature terms in the bulk are generically expected to delocalize gravity.
We consider localization of gravity in smooth domain wall solutions of gravity coupled to a scalar field with a generic potential in the presence of the Gauss-Bonnet term. We discuss conditions on the scalar potential such that domain wall solutions are non-singular. We point out that the presence of the Gauss-Bonnet term does not allow flat solutions with localized gravity that violate the weak energy condition. We also point out that in the presence of the Gauss-Bonnet term infinite tension flat domain walls violate positivity. In fact, for flat solutions unitarity requires that on the solution the scalar potential be bounded below.
We consider an infinite-volume brane world setup where a codimension one brane is coupled to bulk gravity plus a scalar field with vanishing potential. The latter is protected by bulk supersymmetry, which is intact even if brane supersymmetry is completely broken as the volume of the extra dimension is infinite. Within this setup we discuss a flat solution with a ``self-tuning'' property, that is, such a solution exists for a continuous range of values for the brane tension. This infinite-volume solution is free of any singularities, and has the property that the brane cosmological constant is protected by bulk supersymmetry. We, however, also point out that consistency of the coupling between bulk gravity and brane matter generically appears to require that the brane world-volume theory be conformal.
We consider a recently proposed setup where a codimension one brane is embedded in the background of a smooth domain wall interpolating between AdS and Minkowski minima. Since the volume of the transverse dimension is infinite, bulk supersymmetry is intact even if brane supersymmetry is completely broken. On the other hand, in this setup unbroken bulk supersymmetry is incompatible with non-zero brane cosmological constant, so the former appears to protect the latter. In this paper we point out that, to have a consistent coupling between matter localized on the brane and bulk gravity, in this setup generically it appears to be necessary that the brane world-volume theory be conformal. Thus, unbroken bulk supersymmetry appears to actually protect not only the cosmological constant but also conformal invariance on the brane.
We consider localization of gravity in domain wall solutions of Einstein's gravity coupled to a scalar field with a generic potential. We discuss conditions on the scalar potential such that domain wall solutions are non-singular. Such solutions even exist for appropriate potentials which have no minima at all and are unbounded below. Domain walls of this type have infinite tension, while usual kink type of solutions interpolating between two AdS minima have finite tension. Non-singular domain walls with infinite tension might a priori avoid recent ``no-go'' theorems indicating impossibility of supersymmetric embedding of kink type of domain walls in gauged supergravity. We argue that (non-singular) domain walls are stable even if they have infinite tension. This is essentially due to the fact that localization of gravity in smooth domain walls is a Higgs mechanism corresponding to a spontaneous breakdown of translational invariance. We point out that if the scalar potential has no minima and approaches finite negative values at infinity, then higher derivative terms are under control, and do not affect the cosmological constant on the brane which is vanishing for such backgrounds. Nonetheless, we also point out that higher curvature terms generically delocalize gravity, so that the desired lower dimensional Newton's law is no longer reproduced.
We consider a recent proposal to solve the cosmological constant problem within the context of brane world scenarios with infinite volume extra dimensions. In such theories bulk can be supersymmetric even if brane supersymmetry is completely broken. We propose a setup where unbroken bulk supersymmetry appears to protect the brane cosmological constant. This is due to a non-trivial scalar potential in the bulk which implies a non-trivial profile for a bulk scalar field. In the presence of the latter bulk supersymmetry appears to be incompatible with non-vanishing brane cosmological constant. Moreover, in this setup the corresponding domain wall interpolates between an AdS and the Minkowski vacua, so that the weak energy condition is not violated.
We consider a recent proposal to solve the cosmological constant problem within the context of brane world scenarios with infinite volume extra dimensions. In such theories bulk can be supersymmetric even if brane supersymmetry is completely broken. The bulk cosmological constant can therefore naturally be zero. Since the volume of the extra dimensions is infinite, it might appear that at large distances one would measure the bulk cosmological constant which vanishes. We point out a caveat in this argument. In particular, we use a concrete model, which is a generalization of the Dvali-Gabadadze-Porrati model, to argue that in the presence of non-zero brane cosmological constant at large distances such a theory might become effectively four dimensional. This is due to a mass gap in the spectrum of bulk graviton modes. In fact, the corresponding distance scale is set precisely by the brane cosmological constant. This phenomenon appears to be responsible for the fact that bulk supersymmetry does not actually protect the brane cosmological constant.
We discuss geometry underlying orientifolds with non-trivial NS-NS B-flux. If D-branes wrap a torus with B-flux the rank of the gauge group is reduced due to non-commuting Wilson lines whose presence is implied by the B-flux. In the case of D-branes transverse to a torus with B-flux the rank reduction is due to a smaller number of D-branes required by tadpole cancellation conditions in the presence of B-flux as some of the orientifold planes now have the opposite orientifold projection. We point out that T-duality in the presence of B-flux is more subtle than in the case with trivial B-flux, and it is precisely consistent with the qualitative difference between the aforementioned two setups. In the case where both types of branes are present, the states in the mixed (e.g., 59) open string sectors come with a non-trivial multiplicity, which we relate to a discrete gauge symmetry due to non-zero B-flux, and construct vertex operators for the the mixed sector states. Using these results we revisit K3 orientifolds with B-flux (where K3 is a T^4/Z_M orbifold) and point out various subtleties arising in some of these models. For instance, in the Z_2 case the conformal field theory orbifold does not appear to be the consistent background for the corresponding orientifolds with B-flux. This is related to the fact that non-zero B-flux requires the presence of both O5^- as well as O5^+ planes at various Z_2 orbifold fixed points, which appears to be inconsistent with the presence of the twisted B-flux in the conformal field theory orbifold. We also consider four dimensional N=2 and N=1 supersymmetric orientifolds. We construct consistent four dimensional models with B-flux which do not suffer from difficulties encountered in the K3 cases.
We point out that in (open) string compactifications with non-zero NS-NS B-field we can have large Kaluza-Klein thresholds even in the small volume limit. In this limit the corresponding gauge theory description is in terms of a compactification on a non-commutative space (e.g., a torus or an orbifold thereof). Based on this observation we discuss a brane world scenario of non-commutative unification via Kaluza-Klein thresholds. In this scenario, the unification scale can be lowered down to the TeV-range, yet the corresponding compactification radii are smaller than the string length. We discuss a potential application of this scenario in the context of obtaining mixing between different chiral generations which is not exponentially suppressed - as we point out, such mixing is expected to be exponentially suppressed in certain setups with large volume compactifications. We also point out that T-duality is broken by certain non-perturbative twisted open string sectors which are supposed to give rise to chiral generations, so that in the case of a small volume compactification with a rational B-field we cannot T-dualize to a large volume description. In this sense, the corresponding field theoretic picture of unification via Kaluza-Klein thresholds in this setup is best described in the non-commutative language.
We conjecture that a T-dual form of pure QCD describes dynamics of point-like monopoles. T-duality transforms the QCD Lagrangian into a matrix quantum mechanics of zerobranes which we identify with monopoles. At generic points of the monopole moduli space the SU(N) gauge group is broken down to $U(1)^{N-1}$ reproducing the key feature of 't Hooft's Abelian projection. There are certain points in the moduli space where monopole positions coincide, gauge symmetry is enhanced and gluons emerge as massless excitations. We show that there is a linearly rising potential between zerobranes. This indicates the presence of a stretched flux tube between monopoles. The lowest energy state is achieved when monopoles are sitting on top of each other and gauge symmetry is enhanced. In this case they behave as free massive particles and can condense. In fact, we find a constant eigenfunction of the corresponding Hamiltonian which describes condensation of monopoles. Using the monopole quantum mechanics, we argue that large $N$ QCD in this T-dual picture is a theory of a closed bosonic membrane propagating in {\em five} dimensional space-time. QCD point-like monopoles can be regarded in this approach as constituents of the membrane.
Recently it was pointed out that in the TeV-scale brane world there is a logical possibility where the electroweak Higgs can be identified with a fourth generation slepton. In this paper we address various issues in this four-generation TeV-scale Supersymmetric Standard Model with Higgs as a slepton. In particular we discuss how to achieve proton stability by suppressing the corresponding baryon number violating operators via gauging (a discrete subgroup of) the baryon number U(1) symmetry. Dimension five lepton number violating operators which would result in unacceptably large neutrino masses can be similarly suppressed via gauging a discrete subgroup of the lepton number U(1) symmetry. In fact, the four generation feature allows for a novel higher dimensional mechanism for generating small Majorana neutrino masses. We also discuss how to achieve gauge coupling unification, which can be as precise at one loop as in the MSSM, and point out a possible geometric embedding of the corresponding matter content in the brane world context. Finally, we discuss adequate suppression of flavor changing neutral currents in this model, and also point out a novel possibility for supersymmetry breaking via a non-zero F-term of the fourth generation lepton superfield.
We discuss higher loop corrections to gauge coupling renormalization in the context of gauge coupling unification via Kaluza-Klein thresholds. We show that in the case N=1 supersymmetric compactifications the one-loop threshold contributions are dominant, while the higher loop correction are subleading. This is due to the fact that at heavy Kaluza-Klein levels the spectrum as well as the interactions are N=2 supersymmetric. In particular, we give two different arguments leading to this result - one is field theoretic, while the second one utilizes the power of string perturbation techniques. To illustrate our discussions we perform explicit two-loop computations of various corrections to gauge couplings within this framework. We also remark on phenomenological applications of our discussions in the context of TeV-scale brane world.