Non-relativistic String Research Articles

Spin Matrix theory: a quantum mechanical model of the AdS/CFT correspondence

We introduce a new quantum mechanical theory called Spin Matrix theory (SMT). The theory is interacting with a single coupling constant g and is based on a Hilbert space of harmonic oscillators with a spin index taking values in a Lie (super)algebra representation as well as matrix indices for the adjoint representation of U(N). We show that SMT describes N=4 super-Yang-Mills theory (SYM) near zero-temperature critical points in the grand canonical phase diagram. Equivalently, SMT arises from non-relativistic limits of N=4 SYM. Even though SMT is a non-relativistic quantum mechanical theory it contains a variety of phases mimicking the AdS/CFT correspondence. Moreover, the infinite g limit of SMT can be mapped to the supersymmetric sector of string theory on AdS_5 x S^5. We study SU(2) SMT in detail. At large N and low temperatures it is a theory of spin chains that for small g resembles planar gauge theory and for large g a non-relativistic string theory. When raising the temperature a partial deconfinement transition occurs due to finite-N effects. For sufficiently high temperatures the partially deconfined phase has a classical regime. We find a matrix model description of this regime at any coupling g. Setting g=0 it is a theory of N^2+1 harmonic oscillators while for large g it becomes 2N harmonic oscillators.

A nonrelativistic string in superspace-time

Secondary quantizing of the scalar field of an open nonrelativistic string is performed in two-dimensional superspace-time and spontaneous emission of string quanta by the primordial Lemaitre atom is studied.

HOLOGRAPHY OF NON-RELATIVISTIC STRING ON AdS5 × S5

We briefly review a holography of non-relativistic (NR) string on AdS 5× S 5. The NR string can be regarded as a semiclassical string around an AdS2 classical solution corresponding to a straight Wilson line in the gauge-theory side. Exciting non-normalizable modes of the NR string gives source term insertions on the Wilson line. For normalizable modes we discuss a relation to a conformal quantum mechanics.

Non-relativistic strings in expanding spacetime

We obtain a non-relativistic diffeomorphism invariant string action as a special limit of the Nambu–Goto action in a FLRW background. We use this action to study non-relativistic string dynamics in an expanding universe and construct an analytic model describing the macroscopic properties of non-relativistic string networks. The non-relativistic constraint equations allow arbitrarily small string velocities and thus a ‘frustrated’ equation of state for non-interacting strings can be obtained without the need of a velocity damping mechanism. Assuming that colliding string segments reconnect by the exchange of partners, non-relativistic string networks exhibit scaling behaviour, but with enhanced energy densities due to the smaller average string velocity. Non-relativistic string networks can be relevant in several contexts in condensed matter physics and cosmology.

Holography of non-relativistic string on AdS5× S5

We discuss a holographic dual of a non-relativistic (NR) string on AdS5 ? S5 . The NR string can be regarded as a semiclassical string around an AdS2 classical solution corresponding to a straight Wilson line in the gauge-theory side. The quadratic action with respect to the fluctuations is composed of free massive and massless scalars, and free massive fermions on the AdS2 world-sheet. We show that the complete agreement of the spectra between the NR string and a conformal quantum mechanics (CQM). Then we show a holographic relation between normalizable modes of the NR string and wave functions in the CQM. Then it may be argued from this result that an AdS2/CFT1 would be realized in AdS5/CFT4. We can really discuss a GKPW-type relation by considering non-normalizable modes of the NR string in Euclidean signature. Those modes give a source term insertion to the Wilson line, which can also be regarded as a small deformation of it.

Non-relativistic String and D-branes on AdS_5×S^5 from Semiclassical Approximation

Non-relativistic String and D-branes on AdS_5×S^5 from Semiclassical Approximation

Nonrelativistic superstring theories

We construct a supersymmetric version of the ``critical'' non-relativistic bosonic string theory\cite{Kim:2007hb} with its manifest global symmetry. We introduce the anticommuting $bc$ CFT which is the super partner of the $\beta\gamma$ CFT. The conformal weights of the $b$ and $c$ fields are both 1/2. The action of the fermionic sector can be transformed into that of the relativistic superstring theory. We explicitly quantize the theory with manifest SO(8) symmetry and find that the spectrum is similar to that of Type IIB superstring theory. There is one notable difference: the fermions are non-chiral. We further consider ``noncritical'' generalizations of the supersymmetric theory using the superspace formulation. There is an infinite range of possible string theories similar to the supercritical string theories. We comment on the connection between the critical non-relativistic string theory and the lightlike Linear Dilaton theory.

Exotic nonrelativistic string

We construct a classical nonrelativistic string model in 3+1 dimensions. The model contains a spurion tensor field that is responsible for the noncommutative structure of the model. Under double-dimensional reduction the model reduces to the exotic nonrelativistic particle in 2+1 dimensions.

World sheet commutingβγconformal field theory and nonrelativistic string theories

We construct a sigma model in two dimensions with Galilean symmetry in flat target space similar to the sigma model of the critical string theory with Lorentz symmetry in 10 flat spacetime dimensions. This is motivated by the works of Gomis and Ooguri [J. Math. Phys. (N.Y.) 42, 3127 (2001)] and Danielsson et al. [J. High Energy Phys. 10 (2000) 020; J. High Energy Phys. 03 (2001) 041.]. Our theory is much simpler than their theory and does not assume a compact coordinate. This nonrelativistic string theory has a bosonic matter $\ensuremath{\beta}\ensuremath{\gamma}$ conformal field theory with the conformal weight of $\ensuremath{\beta}$ as 1. It is natural to identify time as a linear combination of $\ensuremath{\gamma}$ and $\overline{\ensuremath{\gamma}}$ through an explicit realization of the Galilean boost symmetry. The angle between $\ensuremath{\gamma}$ and $\overline{\ensuremath{\gamma}}$ parametrizes one parameter family of selection sectors. These selection sectors are responsible for having a nonrelativistic dispersion relation without a nontrivial topology in the nonrelativistic setup, which is one of the major differences from the previous works of Gomis and Ooguri and of Danielsson and co-workers. This simple theory is the nonrelativistic analogue of the critical string theory, and there are many different avenues ahead to be investigated. We mention a possible consistent generalization of this theory with different conformal weights for the $\ensuremath{\beta}\ensuremath{\gamma}$ conformal field theory. We also mention supersymmetric generalizations of these theories.

Non-relativistic string and D-branes on AdS5× S5from semiclassical approximation

We show that non-relativistic actions of string and D-branes on AdS_5 x S^5 can be reproduced as a semiclassical approximation of the string and D-brane actions around static 1/2 BPS configurations. This is contrastive to the Penrose limit. For example, the pp-wave string can be recaptured as a semiclassical approximation around a 1/2 BPS particle rotating at the velocity of light. We argue that small deformation of a straight Wilson line would give a composite operator in the gauge-theory side that corresponds to a semiclassical state of the non-relativistic string, according to the semiclassical interpretation.

Non-relativistic superstrings: a new soluble sector of AdS5× S5

We find a new sector of string theory in AdS5 × S5 describing non-relativistic superstrings in that geometry. The worldsheet theory of non-relativistic strings in AdS5 × S5 is derived and shown to reduce to a supersymmetric free field theory in AdS2. Non-relativistic string theory provides a new calculable setting in which to study holography.

Rotating solutions of non-relativistic string theory

We construct classical rotating solutions of non-relativistic string theory. The relation among the energy and angular momenta for these solutions is of the type E = J 2 . Some of the solutions saturate a BPS bound for the energy, they are 1 4 BPS supersymmetric configurations.

Non-relativistic strings and branes as non-linear realizations of Galilei groups

We construct actions for non-relativistic strings and membranes purely as Wess–Zumino terms of the underlying Galilei groups.

A soluble string theory of hadrons

We consider Penrose limits of the Klebanov-Strassler and Maldacena-Nunez holographic duals to N =1 supersymmetric Yang-Mills. By focusing in on the IR region we obtain exactly solvable string theory models. These represent the nonrelativistic motion and low-lying excitations of heavy hadrons with mass proportional to a large global charge. We argue that these hadrons, both physically and mathematically, take the form of heavy nonrelativistic strings; we term them "annulons." A simple toy model of a string boosted along a compact circle allows us considerable insight into their properties. We also calculate the Wilson loop carrying large global charge and show the effect of confinement is quadratic, not linear, in the string tension.

String approximation for the Cooper Pair in high-Tcsuperconductivity

It is assumed that in some sense high-${T}_{c}$ superconductivity is similar to quantum chromodynamics (QCD). This means that the phonons in high-${T}_{c}$ superconductors have a strong interaction between themselves, like they do to gluons in the QCD. At the experimental level this means that in high-${T}_{c}$ superconductors nonlinear sound waves exist. It is possible that the existence of the strong phonon-phonon interaction can lead to the confinement of phonons into a phonon tube (PT) stretched between two Cooper electrons like a hypothesized flux tube between quark and antiquark in the QCD. The flux tube in the QCD leads to a very strong interaction between quark and antiquark, a similar situation can exist in the high-${T}_{c}$ superconductor: the presence of the PT can essentially increase the binding energy for the Cooper pair. In the first rough approximation the PT can be approximated as a nonrelativistic string with Cooper electrons at the ends. The BCS theory with such a potential term is considered. It is shown that the Green's-function method in the superconductivity theory is a realization of the idea Heisenberg proposed for the quantization of a nonlinear spinor field. A possible experimental testing for the string approximation of the Cooper pair is offered.

Remark on the computation of mode sums

The computation of mode sums of the types encountered in basic quantum field theoretic applications is addressed with an emphasis on their expansions into functions of distance that can be interpreted as potentials. We show how to regularize and calculate the Casimir energy for the continuum Nambu-Goto string with massive ends as well as for the discrete Isgur-Paton non-relativistic string with massive ends. As an additional example, we examine the effect on the interquark potential of a constant Kalb-Ramond field strength interacting with a QCD string.

Vibrational modes of a rotating string

Motivated by nonrelativistic models of a QCD (quantum chromodynamic) string, we examine the systemof a nonrelativistic string in uniform rotational motion with one endfixed and with a mass (quark) attached to the other end. A QCD string hasno purely longitudinal modes, so some constraint must be imposed upon thenonrelativistic system to exclude these modes. Accordingly, we examinethe cases that the string is either inextensible or purely transverse. Foreach case we solve first the discretized string and then do the continuumcase. We find the small amplitude oscillatory motions and frequencies ofoscillation of the string and mass. We show that the assumption of a nodeat the end of the inextensible string produces frequencies that are veryclose to the actual frequencies. For the transverse string, we show thatkeeping centrifugal terms for the motion of the masses comprising thestring leads to an unstable mode.PACS Nos.: 03.20.+i, 03.40.-t, 12.39.Mk

BPS dynamics of the triple ( p, q) string junction

We study the dynamics of the triple junction of ( p, q) strings in Type IIB string theory. We probe the tension and mass density of ( p, q) strings by studying harmonic fluctuations of the triple junction. We show that they agree perfectly with the BPS formula provided a suitable geometric interpretation of the junction is given. We provide a precise statement of the BPS limit and force-balance property. At weak coupling and sufficiently dense limit, we argue that a ( p, q) string embedded in the string network is a ‘wiggly string’, whose low-energy dynamics can be described via a renormalization group evolved, smooth effective non-relativistic string. We also suggest the possibility that, upon Type IIB strings being promoted to the M-theory membrane, there can exist ‘evanescent’ bound-states at the triple junction in the continuum.

The quantisation of non-relativistic strings with arbitrary mass and charge densities

The authors present a method for extending charged point particles into strings, within a non-relativistic framework. This method allows a discussion of models with a non-uniform mass and charge distribution, such as strings with quark-like endpoint masses. The form factor associated with a ground-state charged string is calculated, which shows a rapid fall-off with momentum transfer. The authors discuss the question of the second-quantisation of such models.

Canonical quantization of inhomogeneous strings

The canonical quantization procedure for homogeneous nonrelativistic strings is extended to inhomogeneous strings having nonconstant density and tension, in fixed-, free-, and closed-boundary configurations. The general oscillator expansion form of the Hamiltonian is maintained. Possibilities of harmonic spectra and corresponding interactions are explored.