Noncommutative Super Yang-Mills Theory Research Articles

Entanglement wedge cross-section for noncommutative Yang-Mills theory

The signature of noncommutativity on various measures of entanglement has been observed by considering the holographic dual of noncommutative super Yang-Mills theory. We have followed a systematic analytical approach in order to compute the holographic entanglement entropy corresponding to a strip like subsystem of length l. The relationship between the subsystem size (in dimensionless form) frac{l}{a} and the turning point (in dimensionless form) introduces a critical length scale frac{l_c}{a} which leads to three domains in the theory, namely, the deep UV domain (l < lc; aut » 1, aut ∼ aub), deep noncommutative domain (l > lc, aub> aut » 1) and deep IR domain (l > lc, aut « 1). This in turn means that the length scale lc distinctly points out the UV/IR mixing property of the non-local theory under consideration. We have carried out the holographic study of entanglement entropy for each of these domains by employing both analytical and numerical techniques. The broken Lorentz symmetry induced by noncommutativity has motivated us to redefine the entropic c-function. We have obtained the noncommutative correction to the c-function upto leading order in the noncommutative parameter. We have also looked at the behaviour of this quantity over all the domains of the theory. We then move on to compute the minimal cross-section area of the entanglement wedge by considering two dis- joint subsystems A and B. On the basis of EP = EW duality, this leads to the holographic computation of the entanglement of purification. The correlation between two subsystems, namely, the holographic mutual information I(A : B) has also been computed. Moreover, the computations of EW and I(A : B) has been done for each of the domains in the theory. We have then briefly discussed the effect of the UV cut-off on the IR behaviours of these quantities. Finally, we consider a black hole geometry with a noncommutative parameter and study the influence of both noncommutativity and finite temperature on the various measures of quantum entanglement.

T-duality to scattering amplitude and Wilson loop in non-commutative super Yang-Mills theory

We first perform bosonic T-duality transformation on one of the marginal TsT (T-duality, shift, T-duality)-deformed AdS5×S5 spacetime, which corresponds to 4D mathcal{N}=4 non-commutative super Yang-Mills theory (NCSYM). We then construct the solution to Killing spinor equations of the resulting background, and perform the fermionic T-duality transformation. The final dual geometry becomes the usual AdS5 × S5 spacetime but with a constant NS-NS B-field depending on the non-commutative parameter. As applications, we study the gluon scattering amplitude and open string (Wilson loop) solution in the TsT-deformed AdS5 × S5 spacetime, which are dual to the null polygon Wilson loop and the folded string solution respectively in the final dual geometry.

Holographic complexity and noncommutative gauge theory

We study the holographic complexity of noncommutative field theories. The four-dimensional mathcal{N}=4 noncommutative super Yang-Mills theory with Moyal algebra along two of the spatial directions has a well known holographic dual as a type IIB supergravity theory with a stack of D3 branes and non-trivial NS-NS B fields. We start from this example and find that the late time holographic complexity growth rate, based on the “complexity equals action” conjecture, experiences an enhancement when the non-commutativity is turned on. This enhancement saturates a new limit which is exactly 1/4 larger than the commutative value. We then attempt to give a quantum mechanics explanation of the enhancement. Finite time behavior of the complexity growth rate is also studied. Inspired by the non-trivial result, we move on to more general setup in string theory where we have a stack of Dp branes and also turn on the B field. Multiple noncommutative directions are considered in higher p cases.

Notes on holographic Schwinger effect

We use the method of evaluating the decay rate in terms of the imaginary part of a probe brane action to study the holographic Schwinger effect. In the confining D3-branes case, we find that the Schwinger effect occurs at energy scales higher than the Kaluza-Klein mass, indicating the absence of such effect when the dual gauge field theory can be regarded as an 2+1 dimensional theory. This property is independent of the configuration of the probe brane. In the case of D3-branes with a B field dual to a noncommutative super Yang-Mills theory, we study how the decay rate is affected by the noncommutative effect.

On the continuity of the commutative limit of the 4d [formula omitted] non-commutative super Yang–Mills theory

We study the commutative limit of the non-commutative maximally supersymmetric Yang–Mills theory in four dimensions (N=4 SYM), where non-commutativity is introduced in the two spacelike directions. The commutative limits of non-commutative spaces are important in particular in the applications of non-commutative spaces for regularisation of supersymmetric theories (such as the use of non-commutative spaces as alternatives to lattices for supersymmetric gauge theories and interpretations of some matrix models as regularised supermembrane or superstring theories), which in turn can play a prominent role in the study of quantum gravity via the gauge/gravity duality. In general, the commutative limits are known to be singular and non-smooth due to UV/IR mixing effects. We give a direct proof that UV effects do not break the continuity of the commutative limit of the non-commutative N=4 SYM to all order in perturbation theory, including non-planar contributions. This is achieved by establishing the uniform convergence (with respect to the non-commutative parameter) of momentum integrals associated with all Feynman diagrams appearing in the theory, using the same tools involved in the proof of finiteness of the commutative N=4 SYM.

Holography and D3-branes in Melvin universes

Recently, Hashimoto and Thomas [J. High Energy Phys., 01 (2006) 083] found that noncommutative super Yang-Mills (NCSYM) theory with space-dependent noncommutativity can be formulated as a decoupling limit of open strings ending on D3-branes wrapping a Melvin universe supported by a flux of the NSNS B-field. Under S-duality, we show that this theory turns into a noncommutative open string (NCOS) theory with space-dependent space-time noncommutativity and effective space-dependent string scale. It is an NCOS theory with both space-dependent space-space and space-time noncommutativities under more general SL(2,Z) transformation. These space-dependent noncommutative theories (NCSYM and NCOS) have completely the same thermodynamics as that of ordinary super YM theory, NCSYM and NCOS theories with constant noncommutativity in the dual supergravity description. Starting from black D3-brane solution in the Melvin universe and making a Lorentz boost along one of spatial directions on the worldvolume of D3-branes, we show that the decoupled theory is a lightlike NCSYM theory with space-dependent noncommutativity in a static frame or in an infinite-momentum frame depending on whether there is a gravitational pp-wave on the worldvolume of the D3-branes.

D0-D4 brane tachyon condensation to a BPS state and its excitation spectrum in noncommutative super Yang-Mills theory

We investigate the D0-D4-brane system for different B-field backgrounds including the small instanton singularity in noncommutative SYM theory. We discuss the excitation spectrum of the unstable state as well as for the BPS D0-D4 bound state. We compute the tachyon potential which reproduces the complete mass defect. The relevant degrees of freedom are the massless (4,4) strings. Both results are in contrast with existing string field theory calculations. The excitation spectrum of the small instanton is found to be equal to the excitation spectrum of the fluxon solution on R^2_theta x R which we trace back to T-duality. For the effective theory of the (0,0) string excitations we obtain a BFSS matrix model. The number of states in the instanton background changes significantly when the B-field becomes self-dual. This leads us to the proposal of the existence of a phase transition or cross over at self-dual B-field.

Seiberg–Witten Map for Noncommutative Super Yang–Mills Theory

In this paper we derive the Seiberg–Witten map for noncommutative super Yang–Mills theory in Wess–Zumino gauge. Following (and using results of) hep-th/0108045 we split the observer Lorentz transformations into a covariant particle Lorentz transformation and a remainder which gives directly the Seiberg–Witten differential equations. These differential equations lead to a θ-expansion of the noncommutative super Yang–Mills action which is invariant under commutative gauge transformations and commutative observer Lorentz transformation, but not invariant under commutative supersymmetry transformations: The θ-expansion of noncommutative supersymmetry leads to a θ-dependent symmetry transformation. For this reason the Seiberg–Witten map of super Yang–Mills theory cannot be expressed in terms of superfields.

Moduli space and scattering of D0-branes in noncommutative super-Yang–Mills theory

We study the moduli space of the D0-brane system on Dp-branes realized in the noncommutative super-Yang–Mills theory. By examining the fluctuations around the solitonic solutions generated by solution generating technique, we confirm the interpretation of the moduli as the positions of D0-branes on Dp-branes. Low-energy scattering process is also examined for two D0-branes. We find that the D0-branes scatter at right angle for head-on collision in the D0–D4 system. For D0–D6 and D0–D8 systems we find special solutions which reduce to the D0–D4 case, giving the same behavior. This suggests that the scattering at right angle for head-on collision is a universal behavior of this kind of soliton scatterings.

Superpartner solutions of a BPS monopole in noncommutative space

We construct U(2) BPS monopole superpartner solutions in N=2 non-commutative super Yang-Mills theory. Calculation to the second order in the noncommutative parameter $\theta$ shows that there is no electric quadrupole moment that is expected from the magnetic dipole structure of noncommtative U(2) monopole. This might give an example of the nature of how supersymmetry works not changing between the commutative and noncommutative theories.

Supersymmetry, spectrum and fate of D0–D p systems with B-field

It has been shown that D0–D p ( p=2,4,6,8) systems can be BPS in the presence of B-field even if they are not otherwise. We review the number of remaining supersymmetries, the open string ground state spectrum and the construction of the D0–D p systems as solitonic solutions in the noncommutative super-Yang–Mills theory. We derive the complete mass spectrum of the fluctuations to discuss the stability of the systems. The results are found to agree with the analysis in the string picture. In particular, we show that supersymmetry is enhanced in D0–D8 depending on the B-fields and it is consistent with the degeneracy of mass spectrum. We also derive potentials and discuss their implications for these systems.

Dirac–Born–Infeld action, Seiberg–Witten map, and Wilson lines

We write the recently conjectured action for transformation of the ordinary Born–Infeld action under the Seiberg–Witten map with one open Wilson contour in a manifestly noncommutative gauge invariant form. This action contains the nonconstant closed string fields, higher order derivatives of the noncommutative gauge fields through the ∗ N -product, and a Wilson operator. We extend this noncommutative D 9-brane action to the action for D p -brane by transforming it under T-duality. Using this noncommutative D p -brane action we then evaluate the linear couplings of the graviton and dilaton to the brane for arbitrary noncommutative parameters. By taking the Seiberg–Witten limit we show that they reduce exactly to the known results of the energy–momentum tensor of the noncommutative super-Yang–Mills theory. We take this as an evidence that the noncommutative action in the Seiberg–Witten limit includes properly all derivative correction terms.

Wilson loops in strongly coupled noncommutative gauge theories

We discuss Wilson loop averages in 4-dimensional non-commutative superYang-Mills theory using the dual supergravity description. We postulate that the Wilson loops are located at the mimimum length scale $R$ in the fifth radial coordinate. We find that they exhibit a crossover from Coulomb type of behaviour for large loops, for which non-commutativity is unimportant, to area law for small loops, for which non-commutativity effects are large. The string tension, which can be read off from the area law, is controlled by the non-commutativity scale. The crossover itself, however, appears to involve loops of size of order $R$ which is much larger than the non-commutativity scale. The existence of the area law in non-commutative super Yang-Mills theory which persists up to a large crossover length scale provides further evidence for connection to an underlying string theory.

Strong coupling effects in noncommutative spaces from OM theory and supergravity

We show that a four-parameter class of (3+1)-dimensional NCOS theories can be obtained by dimensional reduction on a general 2-torus from OM theory. Compactifying two spatial directions of NCOS theory on a 2-torus, we study the transformation properties under the SO (2,2; Z ) T-duality group. We then discuss non-perturbative configurations of non-commutative super Yang–Mills theory. In particular, we calculate the tension for magnetic monopoles and ( p , q ) dyons and exhibit their six-dimensional origin, and construct a supergravity solution representing an instanton in the gauge theory. We also compute the potential for a monopole–antimonopole in the supergravity approximation.

The IR/UV connection in the non-commutative gauge theories

Quantum field theory on non-commutative spaces does not enjoy the usual ultraviolet-infrared decoupling that forms the basis for conventional renormalization. The high momentum contributions to loop integrations can lead to unfamiliar long distance behavior which can potentially undermine naive expectations for the IR behavior of the theory. These "anomalies" involve non-analytic behavior in the noncommutativity parameter Theta making the limit Theta goes to zero singular. In this paper we will analyze such effects in the one loop approximation to gauge theories on non-commutative space. We will see that contrary to expectations poles in Theta do occur and lead to large discrepancies between the expected and actual infrared behavior. We find that poles in Theta are absent in supersymmetric theories. The "anomalies" are generally still present, but only at the logarithmic level. A notable exception is non-commutative super Yang Mills theory with 16 real supercharges in which anomalous effects seem to be absent altogether.

Noncommutative super Yang–Mills theories with 8 supercharges and brane configurations

In this paper we consider D=4 NCSYM theories with 8 supercharges. We study these theories through a proper type IIA (and M-theory) brane configuration. We find the one loop beta function of these theories and show that there is an elliptic curve describing the moduli space of the theory, which is in principle the same as the curve for the commutative counter-part of our theory. We study some other details of the dynamics by means of this brane configuration.

Noncommutative monopole at the second order in θ

We study the noncommutative U(2) monopole solution at the second order in the noncommutativity parameter \theta^{ij}. We solve the BPS equation in noncommutative super Yang-Mills theory to O(\theta^2), transform the solution to the commutative description by the Seiberg-Witten (SW) map, and evaluate the eigenvalues of the scalar field. We find that, by tuning the free parameters in the SW map, we can make the scalar eigenvalues precisely reproduce the configuration of a tilted D-string suspended between two parallel D3-branes. This gives an example of how the ambiguities inevitable in the higher order SW map are fixed by physical requirements.

A note on interactions of (non-commutative) instantons via AdS/CFT

We consider the interaction between instantons and anti-instantons in four-dimensional N=4 super-Yang–Mills theory at large N and large 't Hooft coupling, as described by D-instantons via AdS/CFT duality. We give an estimate of the strength of the interaction in various regimes. We also discuss the case of non-commutative super-Yang–Mills theory where the interaction between instantons and anti-instantons can be used as a way to probe the locality properties of the theory in the supergravity picture, without explicit reference to the definition of local operators.

Thermodynamics of largeNnoncommutative super Yang-Mills theory

We study the thermodynamics of the large N noncommutative super Yang-Mills theory in the strong 't Hooft coupling limit in the spirit of AdS/CFT correspondence. It has already been noticed that some thermodynamic quantities of near-extremal D3-branes with NS B fields, which are dual gravity configurations of the noncommutative ${\cal N}$=4 super Yang-Mills theory, are the same as those without B fields. In this paper, (1) we examine the $\alpha'^3 R^4$ corrections to the free energy and find that the part of the tree-level contribution remains unchanged, but the one-loop and the non-perturbative D-instanton corrections are suppressed, compared to the ordinary case. (2) We consider the thermodynamics of a bound state probe consisting of D3-branes and D-strings in the near-extremal D3-brane background with B field, and find the thermodynamics of the probe is the same as that of a D3-brane probe in the D3-brane background without B field. (3) The stress-energy tensor of the noncommutative super Yang-Mills theory is calculated via the AdS/CFT correspondence. It is found that the tensor is not isotropic and its trace does not vanish, which confirms that the super Yang-Mills is not conformal even in four dimensions due to the noncommutative nature of space. Our results render further evidence for the argument that the large N noncommutative and ordinary super Yang-Mills theories are equivalent not only in the weak coupling limit, but also in the strong coupling limit.

Matrix theory in a constant C field background

D0-branes moving in a constant antisymmetric C field are found to be described by quantum mechanics of the supersymmetric matrix model with a similarity transformation. Sometimes this similarity transformation is singular or ill-defined and cannot be ignored. As an example, when there are nonvanishing C−ij components, we obtain the theory for Dp-branes which is effectively the noncommutative super Yang–Mills theory. We also briefly discuss the effects of other nonvanishing components such as C+ij and Cijk.