33 research outputs found
An analytic Lifshitz black hole
A Lifshitz point is described by a quantum field theory with anisotropic
scale invariance (but not Galilean invariance). In arXiv:0808.1725, gravity
duals were conjectured for such theories. We construct analytically a black
hole which asymptotes to a vacuum Lifshitz solution; this black hole solves the
equations of motion of some simple (but somewhat strange) extensions of the
models of arXiv:0808.1725. We study its thermodynamics and scalar response
functions. The scalar wave equation turns out to be exactly solvable.
Interestingly, the Green's functions do not exhibit the ultralocal behavior
seen previously in the free Lifshitz scalar theory.Comment: 18 page
Inclusion control in steel castings
“Non-metallic inclusions are mainly comprised of oxides, sulfides, and nitrides, and are formed in liquid steel during the melting and refining process, as a result of reoxidation, worn-out refractories, or entrained slag. The notch toughness of high strength steels is particularly susceptible to the type, number, size, and distribution of non-metallic inclusions. High manganese and aluminum austenitic steels, or Fe-Mn-Al steels, have gained much interest in the military and automotive sector because of their excellent combinations of high strength and toughness. However, these steels are subject to both oxide bifilms and aluminum nitride, AlN, inclusions which form during melting and casting. During the casting process, the gating system plays an important role in determining the casting quality and the overall level of inclusions and bifilm defects. Two solutions to control inclusions during mold filling include molten metal filtration and design of novel “naturally pressurized” gating systems that control metal flow into the casting cavity and reduce air entrainment. However, the use of filters and these naturally pressurized gating systems add an additional cost and generally reduce casting yield. In the current study, the effects of filtration and gating design on reduction of bifilms and inclusions in Fe-Mn-Al steel were determined using two novel mold designs. A parallel gating study involving an aluminum deoxidized, cast composition of SAE 8630 was also performed. The results of this study showed that ceramic foam filters were more effective at removing solid oxide bifilms and aluminum nitride inclusions from Fe-Mn-Al steel castings than the naturally pressurized gating systems. Future studies should be directed at developing naturally pressurized gating systems with filters”--Abstract, page iv
Holographic view of non-relativistic physics
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 167-177).Motivated by the AdS/CFT correspondence for relativistic CFTs, it seems natural to generalize it to non-relativistic CFTs. Such a dual description could provide insight into strong coupling phenomena observed in condensed matter systems. Scale invariance can be realized in non-relativistic theories in many ways. One freedom is the relative scale dimension of time and space, called the dynamical exponent z. In this thesis, we will mainly focus on the case where z = 2, however gravity duals for other values of z have also been found. In the first part of the thesis, we study NRCFTs that are Galilean invariant. Discrete light cone quantization (DLCQ) of V= 4 super Yang-Mills theory is an example of such a system with z = 2 scaling symmetry. A more realistic example of a system with the same set of symmetries is a system of cold fermions at unitarity. These non-relativistic systems respect a symmetry algebra known as the Schrödinger algebra. We propose a gravity dual that realizes the symmetries of the Schrödinger algebra as isometries. An unusual feature of this duality is that the bulk geometry has two extra dimensions than the CFT, instead of the usual one. The additional direction is a compact direction and shift symmetry along this direction corresponds to the particle number transformation. This solution can be embedded into string theory by performing a set of operations (known as the Null-Melvin twist) on AdS5 x S' solution of type IIB supergravity. This method also provides a way of finding a black hole solution which has asymptotic Schrödinger symmetries. The field theory dual of these gravity solutions happens to be a modified version of DLCQ V = 4 super Yang-Mills theory. The thermodynamics of these theories is very different from that of cold atoms. This happens to be a consequence of realizing the entire Schrödinger group as isometries of the spacetime. We give an example of a holographic realization in which the particle number symmetry is realized as a bulk gauge symmetry. In this proposal, the Schrödinger algebra is realized in the bulk without the introduction of an additional compact direction. Using this proposal, we find a confining solution that describes a non-relativistic system at finite density. We use the holographic dictionary to compute the conductivity of this system and it is found to exhibit somewhat unusual behavior. In the second part of the thesis we study gravity duals of Lifshitz theories. These are non-relativistic scale invariant theories that are not boost invariant. These theories do not have a particle number symmetry unlike the boost invariant NRCFTs. We present solutions of 1OD and 111D supergravity theories that are dual to Lifshitz theories. We present a black hole solution that is dual to a strongly interacting Lifshitz theory at finite temperature. We show that the finite temperature correlators in the interacting theories do not exhibit ultra-local behavior which was observed in free Lifshitz theories.by Koushik Balasubramanian.Ph.D
Hot Spacetimes for Cold Atoms
Building on our earlier work and that of Son, we construct string theory
duals of non-relativistic critical phenomena at finite temperature and density.
Concretely, we find black hole solutions of type IIB supergravity whose
asymptotic geometries realize the Schroedinger group as isometries. We then
identify the non-relativistic conformal field theories to which they are dual.
We analyze the thermodynamics of these black holes, which turn out to describe
the system at finite temperature and finite density. The strong-coupling result
for the shear viscosity of the dual non-relativistic field theory saturates the
KSS bound.Comment: latex, 40+1 pages; v2: added subsection 4.6, solidified calculation
of stress tensor, added ref
Gravity duals for non-relativistic CFTs
We attempt to generalize the AdS/CFT correspondence to non-relativistic
conformal field theories which are invariant under Galilean transformations.
Such systems govern ultracold atoms at unitarity, nucleon scattering in some
channels, and more generally, a family of universality classes of quantum
critical behavior. We construct a family of metrics which realize these
symmetries as isometries. They are solutions of gravity with negative
cosmological constant coupled to pressureless dust. We discuss realizations of
the dust, which include a bulk superconductor. We develop the holographic
dictionary and compute some two-point correlators. A strange aspect of the
correspondence is that the bulk geometry has two extra noncompact dimensions.Comment: 12 pages; v2, v3, v4: added references, minor corrections; v3:
cleaned up and generalized dust; v4: closer to published versio
String theory duals of Lifshitz-Chern-Simons gauge theories
We propose candidate gravity duals for a class of non-Abelian z=2 Lifshitz
Chern-Simons (LCS) gauge theories studied by Mulligan, Kachru and Nayak. These
are nonrelativistic gauge theories in 2+1 dimensions in which parity and
time-reversal symmetries are explicitly broken by the presence of a
Chern-Simons term. We show that these field theories can be realized as
deformations of DLCQ N=4 super Yang-Mills theory. Using the holographic
dictionary, we identify the bulk fields that are dual to these deformations.
The geometries describing the groundstates of the non-Abelian LCS gauge
theories realized here exhibit a mass gap.Comment: 25+14 pages, 3 figures; v2: significant corrections regarding IR
geometry, resulting in new section 5; journal versio
Lifshitz spacetimes from AdS null and cosmological solutions
We describe solutions of 10-dimensional supergravity comprising null
deformations of with a scalar field, which have
Lifshitz symmetries. The bulk Lifshitz geometry in 3+1-dimensions arises by
dimensional reduction of these solutions. The dual field theory in this case is
a deformation of the N=4 super Yang-Mills theory. We discuss the holographic
2-point function of operators dual to bulk scalars. We further describe
time-dependent (cosmological) solutions which have anisotropic Lifshitz scaling
symmetries. We also discuss deformations of in 11-dimensional
supergravity, which are somewhat similar to the solutions above. In some cases
here, we expect the field theory duals to be deformations of the Chern-Simons
theories on M2-branes stacked at singularities.Comment: Latex, 29pgs, v3. references, minor clarifications (subsection on
Lifshitz geometry seen by scalar probes) added, to appear in JHE