Terms Of Branes Research Articles

Lorentz violation in warped extra dimensions

Higher dimensional theories which address some of the problematic issues of the Standard Model(SM) naturally involve some form of $D=4+n$-dimensional Lorentz invariance violation (LIV). In such models the fundamental physics which leads to, e.g., field localization, orbifolding, the existence of brane terms and the compactification process all can introduce LIV in the higher dimensional theory while still preserving 4-d Lorentz invariance. In this paper, attempting to capture some of this physics, we extend our previous analysis of LIV in 5-d UED-type models to those with 5-d warped extra dimensions. To be specific, we employ the 5-d analog of the SM Extension of Kostelecky et. al. ~which incorporates a complete set of operators arising from spontaneous LIV. We show that while the response of the bulk scalar, fermion and gauge fields to the addition of LIV operators in warped models is qualitatively similar to what happens in the flat 5-d UED case, the gravity sector of these models reacts very differently than in flat space. Specifically, we show that LIV in this warped case leads to a non-zero bulk mass for the 5-d graviton and so the would-be zero mode, which we identify as the usual 4-d graviton, must necessarily become massive. The origin of this mass term is the simultaneous existence of the constant non-zero $AdS_5$ curvature and the loss of general co-ordinate invariance via LIV in the 5-d theory. Thus warped 5-d models with LIV in the gravity sector are not phenomenologically viable.

Gauge/gravity duality applied to condensed matter systems

AbstractIn this review we investigate phenomena of strongly‐coupled quantum critical theories, which also appear in condensed matter systems. Using the AdS/CFT correspondence, a technique motivated by string theory, the strongly‐coupled scale‐invariant theories can be related to gravity theories at weak coupling. Within this framework we study the holographic description of superconductors and the emerging fermi surface of strongly coupled fermions. We also calculate the conductivity of alternating currents and determine the direct current conductivity for (non‐) relativistic systems beyond linear response. Since the explicit string theory construction in terms of probe branes embedded in type IIB supergravity is explicitly known, we are able to identify the dual operators on the field theory side and can compare the effects at weak and strong coupling.

Free particles from Brauer algebras in complex matrix models

The gauge invariant degrees of freedom of matrix models based on an N x N complex matrix, with U(N) gauge symmetry, contain hidden free particle structures. These are exhibited using triangular matrix variables via the Schur decomposition. The Brauer algebra basis for complex matrix models developed earlier is useful in projecting to a sector which matches the state counting of N free fermions on a circle. The Brauer algebra projection is characterized by the vanishing of a scale invariant laplacian constructed from the complex matrix. The special case of N=2 is studied in detail: the ring of gauge invariant functions as well as a ring of scale and gauge invariant differential operators are characterized completely. The orthonormal basis of wavefunctions in this special case is completely characterized by a set of five commuting Hamiltonians, which display free particle structures. Applications to the reduced matrix quantum mechanics coming from radial quantization in N=4 SYM are described. We propose that the string dual of the complex matrix harmonic oscillator quantum mechanics has an interpretation in terms of strings and branes in 2+1 dimensions.

Covariant gravitational dynamics in 3+1+1 dimensions

We develop a 3+1+1 covariant formalism with cosmological and astrophysical applications. First we give the evolution and constraint equations both on the brane and off-brane in terms of 3-space covariant kinematical, gravito-electro-magnetic (Weyl) and matter variables. We discuss the junction conditions across the brane in terms of the new variables. Then we establish a closure condition for the equations on the brane. We also establish the connection of this formalism with isotropic and anisotropic cosmological brane-worlds. Finally we derive a new brane solution in the framework of our formalism: the tidal charged Taub-NUT-(A)dS brane, which obeys the closure condition.

THE HIERARCHY PROBLEM, RADION MASS, LOCALIZATION OF GRAVITY AND 4D EFFECTIVE NEWTONIAN POTENTIAL IN STRING THEORY ON S1/Z2

In this paper, we present a systematical study of braneworlds of string theory on S1/Z2. In particular, starting with the toroidal compactification of the Neveu–Schwarz/Neveu–Schwarz sector in D + d dimensions, we first obtain an effective D-dimensional action, and then compactify one of the D - 1 spatial dimensions by introducing two orbifold branes as its boundaries. We divide the whole set of the gravitational and matter field equations into two groups, one holds outside the two branes, and the other holds on them. By combining the Gauss–Codacci and Lanczos equations, we write down explicitly the general gravitational field equations on each of the two branes, while using distribution theory we express the matter field equations on the branes in terms of the discontinuities of the first derivatives of the matter fields. Afterwards, we address three important issues: (i) the hierarchy problem; (ii) the radion mass; and (iii) the localization of gravity, the four-dimensional Newtonian effective potential and the Yukawa corrections due to the gravitational high-order Kaluza–Klein (KK) modes. The mechanism of solving the hierarchy problem is essentially the combination of the large extra dimension and warped factor mechanisms together with the tension coupling scenario. With very conservative arguments, we find that the radion mass is of the order of 10-2 GeV. The gravity is localized on the visible brane, and the spectrum of the gravitational KK modes is discrete and can be of the order of TeV. The corrections to the four-dimensional Newtonian potential from the higher order of gravitational KK modes are exponentially suppressed and can be safely neglected in current experiments. In an appendix, we also present a systematical and pedagogical study of the Gauss–Codacci equations and Israel's junction conditions across a (D - 1)-dimensional hypersurface, which can be either spacelike or timelike.

Higher curvature brane corrections to the DGP model

We investigate the Dvali–Gabadadze–Porrati (DGP) model corrected by higher curvature brane terms. We show that these corrections have a dramatic impact on the spectrum of the model at the linearized level. Owing to the presence of higher derivatives in the field equations very massive ghost excitations with mass of order of Planck mass are generated in the ordinary branch of the model. These excitations describe an instability of Minkowski vacuum with time-scale of order of the Hubble time H0−1. At large distances these tachyonic excitations are expected to decouple from brane-localized matter. Our modified DGP model represents therefore a very promising framework for solving of the cosmological constant problem, in which Planck scale physics is responsible for the elementary excitations driving the accelerated expansion of the universe, but the time-scale of the instability is settled by gravitational physics at large scales.

HAWKING RADIATION OF FERMIONS VIA TUNNELING FROM A (4+n)-DIMENSIONAL ROTATING BLACK HOLE

We study Hawking radiation of fermions from a (4+n)-dimensional rotating black hole on the brane in terms of the fermions tunneling formalism, proposed by Kerner and Mann recently. To choose the Gamma matrices properly and avoid the ergosphere dragging effect, we perform it in the dragging coordinate frame. We obtain the tunneling rate and emission temperature of fermions which are consistent with the case of scalar particles as expected.

On the geometry of metastable supersymmetry breaking

We give a concise geometric recipe for constructing D-brane gauge theories that exhibit metastable SUSY breaking. We present two simple examples in terms of branes at deformed CY singularities.

SINGLE-BRANE WORLD WITH STABILIZED EXTRA DIMENSION

We present a model describing a single brane with tension embedded into a five-dimensional space–time with compact extra dimension, which can be easily stabilized. We examine the linearized gravity in the model and obtain an expression for the four-dimensional Planck mass on the brane in terms of the model parameters. It is also shown that the scalar sector of the effective four-dimensional theory contains a tachyonic mode, and we discuss the problem of stability of the model.

Moduli stabilization in heterotic M-theory

We reconsider the ingredients of moduli stabilization in heterotic M-theory. On this line we close a gap in the literature deriving the Kähler potential dependence on vector bundle moduli and charged matter. Crucial in this derivation is our superspace formulation of 5d heterotic M-theory taking into account the Bianchi identities modified by brane terms. Likewise, we obtain the Fayet–Iliopolous terms due to brane localised anomalous U(1)'s. After assembling perturbative and non-perturbative contributions to the superpotential, we study supersymmetric (AdS) vacua. It is found that the susy condition decouples the bundle moduli from the geometric moduli. We show that M-theory supersymmetric vacua without five-branes can be found, albeit not at phenomenologically interesting values of the geometric moduli. This result is fairly independent of the choice of vector bundle at the observable brane.

HOLOGRAPHIC FLAVOR IN THEORIES WITH EIGHT SUPERCHARGES

We review the holographic duals of gauge theories with eight supercharges obtained by adding very few flavors to pure supersymmetric Yang–Mills with 16 supercharges. Assuming a brane-probe limit, the gravity duals are engineered in terms of probe branes (the so-called flavor brane) in the background of the color branes. Both types of branes intersect on a given subspace in which the matter is confined. The gauge theory dual is thus the corresponding flavoring of the gauge theory with 16 supercharges. Those theories have in general a nontrivial phase structure; which is also captured in a beautiful way by the gravity dual. Along the lines of the gauge/gravity duality, we review also some of the results on the meson spectrum in the different phases of the theories.

Stringy NJL and Gross-Neveu models at finite density and temperature

Nonlocal stringy versions of the Nambu-Jona-Lasinio and Gross-Neveu models arise in a certain limit of holographic QCD. We analyze the phase structure at finite density and temperature at strong coupling in terms of probe branes in the gravity dual. Comparison with the phase structure of the local field theory models shows qualitative agreement with some aspects, and disagreement with others. Finally, we explain how to construct the Landau potentials for these models by taking the probe branes off-shell.

Fractional brane state in the early Universe

In the early Universe matter was crushed to high densities, in a manner similar to that encountered in gravitational collapse to black holes. String theory suggests that the large entropy of black holes can be understood in terms of fractional branes and antibranes. We assume a similar physics for the matter in the early Universe, taking a toroidal compactification and letting branes wrap around the cycles of the torus. We find an equation of state pi = wiρ, for which the dynamics can be solved analytically. For black holes, fractionation can lead to non-local quantum gravity effects across length scales of order of the horizon radius; similar effects in the early Universe might change our understanding of cosmology in basic ways.

The Gross–Neveu model from string theory

We study an intersecting D-brane model which at low energies describes ( 1 + 1 ) -dimensional chiral fermions localized at defects on a stack of N c D4-branes. Fermions at different defects interact via exchange of massless ( 4 + 1 ) -dimensional fields. At weak coupling this interaction gives rise to the Gross–Neveu (GN) model and can be studied using field theoretic techniques. At strong coupling one can describe the system in terms of probe branes propagating in a curved background in string theory. The chiral symmetry is dynamically broken at zero temperature and is restored above a critical temperature T c which depends on the coupling. The phase transition at T c is first order at strong coupling and second order at weak coupling.

$$\mathbb{C}^2/\mathbb{Z}_{n}$$ Fractional Branes and Monodromy

We construct geometric representatives for the C^2/Z_n fractional branes in terms of branes wrapping certain exceptional cycles of the resolution. In the process we use large radius and conifold-type monodromies, and also check some of the orbifold quantum symmetries. We find the explicit Seiberg-duality which connects our fractional branes to the ones given by the McKay correspondence. We also comment on the Harvey-Moore BPS algebras.

Effective description of brane terms in extra dimensions

We study how theories defined in (extra-dimensional) spaces with localized defects can be described perturbatively by effective field theories in which the width of the defects vanishes. These effective theories must incorporate a ``classical'' renormalization, and we propose a renormalization prescription a la dimensional regularization for codimension 1, which can be easily used in phenomenological applications. As a check of the validity of this setting, we compare some general predictions of the renormalized effective theory with those obtained in a particular ultraviolet completion based on deconstruction.

BABY UNIVERSES AND STRING THEORY

The description of 4D BPS black holes in terms of branes wrapped on various cycles in a Calabi–Yau space gives us the opportunity to study various issues in quantum gravity in a definite way by means of the worldvolume theory of the branes. In the particular example discussed here, there is a simple worldvolume description in terms of 2D Yang–Mills theory. The latter is an exactly solvable system of free fermions in one dimension. The exact answer for the free energy of this system can be written in a way that suggests an interpretation in terms of contributions from multiple (baby) universes.

Computing Wilson lines with dielectric branes

Wilson lines in N = 4 SYM can be computed in terms of branes carrying electric flux, i.e. F-strings dissolved in their worldvolumes. It is then natural to think that those configurations are the effective description of strings expanding due to dielectric effect to D-branes. In this note we explicitly show this for a class of such configurations, namely those dual to Wilson lines either in the symmetric or in the antisymmetric tensor product of fundamentals.

On gravitational description of Wilson lines

We study solutions of Type IIB supergravity, which describe the geometries dual to supersymmetric Wilson lines in N=4 super-Yang-Mills. We show that the solutions are uniquely specified by one function which satisfies a Laplace equation in two dimensions. We show that if this function obeys a certain Dirichlet boundary condition, the corresponding geometry is regular, and we find a simple interpretation of this boundary condition in terms of D3 and D5 branes which are dissolved in the geometry. While all our metrics have AdS_5 x S^5 asymptotics, they generically have nontrivial topologies, which can be uniquely specified by a set of non-contractible three- and five-spheres.

Gravitational field equations in a braneworld with Euler–Poincaré term

We present the effective gravitational field equations in a 3-braneworld with Euler–Poincaré term and a cosmological constant in the bulk spacetime. The similar equations on a 3-brane with symmetry embedded in a five-dimensional bulk spacetime were obtained earlier by Maeda and Torii using the Gauss–Codazzi projective approach in the framework of the Gaussian normal coordinates. We recover these equations on the brane in terms of differential forms and using a more general coordinate setting in the manner of Arnowitt, Deser and Misner (ADM). The latter allows for acceleration of the normals to the brane surface through the lapse function and the shift vector. We show that the gravitational effects of the bulk space are transmitted to the brane through the projected ‘electric’ 1-form field constructed from the conformal Weyl curvature 2-form of the bulk space. We also derive the evolution equations into the bulk space for the electric 1-form field, as well as for the ‘magnetic’ 2-form field parts of the bulk Riemann curvature 2-form. As expected, unlike on-brane equations, the evolution equations involve terms determined by the nonvanishing acceleration of the normals in the ADM-type slicing of spacetime.