We review in detail a number of approaches that have been adopted to try and explain the remarkable observation of our accelerating universe. In particular we discuss the arguments for and recent progress made towards understanding the nature of dark energy. We review the observational evidence for the current accelerated expansion of the universe and present a number of dark energy models in addition to the conventional cosmological constant, paying particular attention to scalar field models such as quintessence, K-essence, tachyon, phantom and dilatonic models. The importance of cosmological scaling solutions is emphasized when studying the dynamical system of scalar fields including coupled dark energy. We study the evolution of cosmological perturbations allowing us to confront them with the observation of the Cosmic Microwave Background and Large Scale Structure and demonstrate how it is possible in principle to reconstruct the equation of state of dark energy by also using Supernovae Ia observational data. We also discuss in detail the nature of tracking solutions in cosmology, particle physics and braneworld models of dark energy, the nature of possible future singularities, the effect of higher order curvature terms to avoid a Big Rip singularity, and approaches to modifying gravity which leads to a late-time accelerated expansion without recourse to a new form of dark energy.

Dynamics of dark energy

http://inspirehep.net/record/499969/files/arXiv:hep-th_9905111.pdf

Large N Field Theories, String Theory and Gravity

We revisit the singular IIB supergravity solution describing M fractional 3branes on the conifold [hep-th/0002159]. Its 5-form flux decreases, which we explain by showing that the relevant N = 1 SUSY SU(N+M)×SU(N) gauge theory undergoes repeated Seiberg-duality transformations in which N → N − M. Far in the IR the gauge theory confines; its chiral symmetry breaking removes the singularity of hep-th/0002159 by deforming the conifold. We propose a non-singular pure-supergravity background dual to the field theory on all scales, with small curvature everywhere if the ‘t Hooft coupling gsM is large. In the UV it approaches that of hep-th/0002159, incorporating the logarithmic flow of couplings. In the IR the deformation of the conifold gives a geometrical realization of chiral symmetry breaking and confinement. We suggest that pure N = 1 Yang-Mills may be dual to strings propagating at small gsM on a warped deformed conifold. We note also that the standard model itself may lie at the base of a duality cascade.

http://iopscience.iop.org/article/10.1088/1126-6708/2000/08/052/pdf

Supergravity and a confining gauge theory: duality cascades and χSB-resolution of naked singularities

Ads/CFT correspondence and symmetry breaking

We develop techniques to compute higher loop string amplitudes for twistedN=2 theories withĉ=3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a particular realization of theN=2 theories, the resulting string field theory is equivalent to a topological theory in six dimensions, the Kodaira-Spencer theory, which may be viewed as the closed string analog of the Chern-Simons theory. Using the mirror map this leads to computation of the ‘number’ of holomorphic curves of higher genus curves in Calabi-Yau manifolds. It is shown that topological amplitudes can also be reinterpreted as computing corrections to superpotential terms appearing in the effective 4d theory resulting from compactification of standard 10d superstrings on the correspondingN=2 theory. Relations withc=1 strings are also pointed out.

Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes

The authors review some aspects of the interplay between the dynamics of branes in string theory and the classical and quantum physics of gauge theories with different numbers of supersymmetries in various dimensions.

Brane dynamics and gauge theory

Entanglement as a probe of confinement

We study string propagation on $AdS_3$ times a compact space from an ``old fashioned'' worldsheet point of view of perturbative string theory We derive the spacetime CFT and its Virasoro and current algebras, thus establishing the conjectured $AdS$/CFT correspondence for this case in the full string theory Our results have implications for the extreme IR limit of the $D1-D5$ system, as well as to 2+1 dimensional BTZ black holes and their Bekenstein-Hawking entropy

https://www.intlpress.com/site/pub/files/_fulltext/journals/atmp/1998/0002/0004/ATMP-1998-0002-0004-a003.pdf

comments on string theory on $AdS_3$

The study of open string tachyon condensation in string field theory can be drastically simplified by making an appropriate choice of coordinates on the space of string fields. We show that a very natural coordinate system is suggested by the connection between the worldsheet renormalization group and spacetime physics. In this system only one field, the tachyon, condenses while all other fields have vanishing expectation values. These coordinates are also well-suited to the study of D-branes as solitons. We use them to show that the tension of the D25-brane is cancelled by tachyon condensation and compute exactly the profiles and tensions of lower dimensional D-branes.

https://iopscience.iop.org/article/10.1088/1126-6708/2000/10/045/pdf

David Kutasov

Papers

Brane dynamics and gauge theory

Entanglement as a probe of confinement

comments on string theory on $AdS_3$

Some exact results on tachyon condensation in string field theory

Seiberg duality in Chern–Simons theory