Corneliu Sochichiu

Two phases of the noncommutative quantum mechanics

We consider quantum mechanics on the noncommutative plane in the presence of magnetic field B. We show, that the model has two essentially different phases separated by the point Bθ=cℏ2/e, where θ is a parameter of noncommutativity. In this point the system reduces to exactly-solvable one-dimensional system. When κ=1−eBθ/cℏ2 0 the number of states is infinite. The perturbative spectrum near the critical point κ=0 is computed.

Taking off the square root of Nambu–Goto action and obtaining Filippov–Lie algebra gauge theory action

We propose a novel prescription to take off the square root of the Nambu–Goto action for a p-brane, which generalizes the Brink–Di Vecchia–Howe–Tucker, also known as the Polyakov method. With an arbitrary decomposition, d+n=p+1, our resulting action is a modified d-dimensional Polyakov action, which is gauged and possesses a Nambu n-bracket squared potential. We first spell out how the (p+1)-dimensional diffeomorphism is realized in the lower dimensional action. Then we discuss a possible gauge fixing of it to a direct product of d-dimensional diffeomorphism and n-dimensional volume preserving diffeomorphism. We show that the latter naturally leads to a novel Filippov–Lie n-algebra based gauge theory action in d dimensions.

SL(2) spin chain and spinning strings on

Abstract We derive the coherent state representation of the integrable spin chain Hamiltonian with symmetry group SL ( 2 , R ) . By passing to the continuum limit, we find a spin chain sigma model describing a string moving on the hyperboloid SL ( 2 , R ) / U ( 1 ) . The same sigma model is found by considering strings rotating with large angular momentum in AdS 5 × S 5 . The spinning strings are identified with semiclassical coherent states built out of SL ( 2 , R ) spin chain states.

SL(2) spin chain and spinning strings on AdS5×S5

Abstract We derive the coherent state representation of the integrable spin chain Hamiltonian with symmetry group SL ( 2 , R ) . By passing to the continuum limit, we find a spin chain sigma model describing a string moving on the hyperboloid SL ( 2 , R ) / U ( 1 ) . The same sigma model is found by considering strings rotating with large angular momentum in AdS 5 × S 5 . The spinning strings are identified with semiclassical coherent states built out of SL ( 2 , R ) spin chain states.

Spin bit models from non-planar N = 4 SYM

Abstract We study spin models underlying the non-planar dynamics of N = 4 SYM gauge theory. In particular, we derive the non-local spin chain Hamiltonian corresponding to the generator of dilatations in the gauge theory at leading order in g YM 2 N but exact in 1 N . States in our spin chain-like model are characterized by a spin-configuration as well as by a linking variable which describes how sites are connected in the chains. Joining and splitting of string/traces is implemented by a twist operator acting on the linking variable. The obtained model is used for the systematic study of non-planar anomalous dimensions and operator mixing in N = 4 SYM. Beyond other, we identify a sequence of SYM operators for which corrections to the one-loop anomalous dimensions stop at the first 1 N non-planar order.

Noncommutative tachyonic solitons. Interaction with gauge field

We show that in the presence of U(1) non-commutative YM interaction the non-commutative tachyonic system exhibits solitonic solutions (even) for finite value of noncommutativity parameter ?.

M[any] vacua of IIB

Description of the spectrum of fluctuations around a commutative vacuum solution, as well as around a solution with degenerate commutator in IIB matrix model is given in terms of supersymmetric-Yang-Mills (YM) model. We construct explicitly the map from hermitean matrices to YM fields and study the dependence of the spectrum and respective YM model on the symmetries of the solution. The gauge algebra of the YM model is shown to contain local reparameterisation algebra as well as Virasoro one.

On matrix models for anomalous dimensions of super-Yang–Mills theory

We consider the matrix model approach to the anomalous dimension matrix in N=4 super-Yang–Mills theory. We construct the path integral representation for the anomalous dimension density matrix and analyze the resulting action. In particular, we consider the large N limit, which results in a classical field theory. Since the same limit leads to spin chains, we propose to consider the former as an alternative description of the latter. We consider also the limit of small N, which corresponds to the restriction to the diagrams of maximal topological genus.

Fermion Doubling and Berenstein-Maldacena-Nastase Correspondence

Abstract We show that the string bit model suffers from doubling in the fermionic sector. The doubling leads to strong violation of supersymmetry in the limit N →∞. Since there is an exact correspondence between string bits and the algebra of BMN operators even at finite N , doubling is expected also on the side of super-Yang–Mills theory. We discuss the origin of the doubling in the BMN sector.

On the equivalence of noncommutative models in various dimensions and brane condensation

Here we construct a map from the algebra of fields in two-dimensional noncommutative of U(1) Yang-Mills fields interacting with Kaluza-Klein scalars to a D-dimensional one, as a solution in the two-dimensional model. This proves the equivalence of noncommutative models in various (even) dimensions. Physically this map describes condensation of D1-branes.