http://cds.cern.ch/record/994225/files/0610327.pdf

Four-dimensional string compactifications with D-branes, orientifolds and fluxes

▪ Abstract We provide a pedagogical introduction to a recently studied class of phenomenologically interesting string models known as Intersecting D-Brane Models. The gauge fields of the Standard Model are localized on D-branes wrapping certain compact cycles on an underlying geometry, whose intersections can give rise to chiral fermions. We address the basic issues and also provide an overview of the recent activity in this field. This article is intended to serve non-experts with explanations of the fundamental aspects of string phenomenology and also to provide some orientation for both experts and non-experts in this active field.

/pdf/toward-realistic-intersecting-d-brane-models-37ilosroqc.pdf

Toward realistic intersecting d-brane models

In this review we describe our current understanding of the properties of open string tachyons on an unstable D-brane or brane–antibrane system in string theory. The various string theoretic methods used for this study include techniques of two-dimensional conformal field theory, open string field theory, boundary string field theory, noncommutative solitons, etc. We also describe various attempts to understand these results using field theoretic methods. These field theory models include toy models like singular potential models and p-adic string theory, as well as more realistic version of the tachyon effective action based on Dirac–Born–Infeld type action. Finally we study closed string background produced by the "decaying" unstable D-branes, both in the critical string theory and in the two-dimensional string theory, and describe the open string completeness conjecture that emerges out of this study. According to this conjecture the quantum dynamics of an unstable D-brane system is described by an int...

Tachyon Dynamics in Open String Theory

We show, using strong subadditivity and Lorentz covariance, that in three-dimensional space-time the entanglement entropy of a circle is a concave function. This implies the decrease of the coefficient of the area term and the increase of the constant term in the entropy between the ultraviolet and infrared fixed points. This is in accordance with recent holographic $c$ theorems and with conjectures about the renormalization group flow of the partition function of a three sphere ($F$ theorem). The irreversibility of the renormalization group flow in three dimensions would follow from the argument provided there is an intrinsic definition for the constant term in the entropy at fixed points. We discuss the difficulties in generalizing this result for spheres in higher dimensions.

Renormalization group running of the entanglement entropy of a circle

We study the large-N gauged quantum mecchanics for a single hermitean matrix in the Harmonic oscillator potential well as a toy model for the AdS/CFT correspondence We argue that the dual geometry should be a string in two dimensions with a curvature of stringy size Even though the dual geometry is not weakly curved, one can still gain knowledge of the system from a detailed study of the open-closed string duality We give a mapping between the basis of states made of traces (closed strings) and the eigenvalues of the matrix (D-brane picture) in terms of Schur polynomials This is interpreted as an exact open-closed duality We connect this model with a decoupling limit of = 4 SYM and the study of giant gravitons in AdS5 ? S5 We show that the two giant gravitons that expand along AdS5 and S5 can be interpreted in the matrix model as taking an eigenvalue from the Fermi sea and exciting it very much, or as making a hole in the Fermi sea respectively This is similar to recent studies of the c = 1 string This connection gives new insight on how to perform calculations for giant gravitons

http://iopscience.iop.org/article/10.1088/1126-6708/2004/07/018/pdf

A toy model for the AdS/CFT correspondence

We consider unstable D0-branes of two dimensional string theory, described by the boundary state of Zamolodchikov and Zamolodchikov [36] multiplied by the Neumann boundary state for the time coordinate t. In the dual description in terms of the c = 1 matrix model, this D0-brane is described by a matrix eigenvalue on top of the upside down harmonic oscillator potential. As suggested by McGreevy and Verlinde [25], an eigenvalue rolling down the potential describes D-brane decay. As the eigenvalue moves down the potential to the asymptotic region it can be described as a free relativistic fermion. Bosonizing this fermion we get a description of the state in terms of a coherent state of the tachyon field in the asymptotic region, up to a non-local linear field redefinition by an energy-dependent phase. This coherent state agrees with the exponential of the closed string one-point function on a disk with Sen's marginal boundary interaction for t which describes D0-brane decay.

D-brane decay in two-dimensional string theory

We consider unstable D0-branes of two dimensional string theory, described by the boundary state of Zamolodchikov and Zamolodchikov [hep-th/0101152] multiplied by the Neumann boundary state for the time coordinate $t$. In the dual description in terms of the $c=1$ matrix model, this D0-brane is described by a matrix eigenvalue on top of the upside down harmonic oscillator potential. As suggested by McGreevy and Verlinde [hep-th/0304224], an eigenvalue rolling down the potential describes D-brane decay. As the eigenvalue moves down the potential to the asymptotic region it can be described as a free relativistic fermion. Bosonizing this fermion we get a description of the state in terms of a coherent state of the tachyon field in the asymptotic region, up to a non-local linear field redefinition by an energy-dependent phase. This coherent state agrees with the exponential of the closed string one-point function on a disk with Sen's marginal boundary interaction for $t$ which describes D0-brane decay.

D-brane Decay in Two-Dimensional String Theory

Renyi entropies S
 q
 are useful measures of quantum entanglement; they can be calculated from traces of the reduced density matrix raised to power q, with q ≥ 0. For (d + 1)-dimensional conformal field theories, the Renyi entropies across S
 d−1 may be extracted from the thermal partition functions of these theories on either (d + 1)-dimensional de Sitter space or $ \mathbb{R} \times {\mathbb{H}^d} $
 , where $ {\mathbb{H}^d} $
 is the d-dimensional hyperbolic space. These thermal partition functions can in turn be expressed as path integrals on branched coverings of the (d + 1)-dimensional sphere and S
 1×
 $ {\mathbb{H}^d} $
 , respectively. We calculate the Renyi entropies of free massless scalars and fermions in d = 2, and show how using zeta-function regularization one finds agreement between the calculations on the branched coverings of S
 3 and on S
 1 × $ {\mathbb{H}^2} $
 . Analogous calculations for massive free fields provide monotonic interpolating functions between the Renyi entropies at the Gaussian and the trivial fixed points. Finally, we discuss similar Renyi entropy calculations in d > 2.

https://dash.harvard.edu/bitstream/handle/1/10860096/Sachdev_Renyi.pdf?sequence=1

Rényi entropies for free field theories

Proton decay in intersecting D-brane models

We analyze proton decay via dimension six operators in certain GUT-like models derived from Type IIA orientifolds with $D6$-branes. The amplitude is parametrically enhanced by a factor of $\alpha_{GUT}^{-1/3}$ relative to the coresponding result in four-dimensional GUT's. Nonetheless, even assuming a plausible enhancement from the threshold corrections, we find little overall enhancement of the proton decay rate from dimension six operators, so that the predicted lifetime from this mechanism remains close to $10^{36}$ years.

Igor R. Klebanov

Papers

D-brane decay in two-dimensional string theory

D-brane Decay in Two-Dimensional String Theory

Rényi entropies for free field theories

Proton decay in intersecting D-brane models

Proton Decay in Intersecting D-brane Models