arXiv subjects

Alok Kumar

Publications and source records attributed to Alok Kumar.

At least 55 records · Page 3Linked to original sources

arXiv2000

Towards Understanding the Predictability of Stock Markets from the Perspective of Computational Complexity

This paper initiates a study into the century-old issue of market predictability from the perspective of computational complexity. We develop a simple agent-based model for a stock market where the agents are traders equipped with simple trading strategies, and their trades together determine the stock prices. Computer simulations show that a basic case of this model is already capable of generating price graphs which are visually similar to the recent price movements of high tech stocks. In the general model, we prove that if there are a large number of traders but they employ a relatively small number of strategies, then there is a polynomial-time algorithm for predicting future price movements with high accuracy. On the other hand, if the number of strategies is large, market prediction becomes complete in two new computational complexity classes CPP and BCPP, which are between P^NP[O(log n)] and PP. These computational completeness results open up a novel possibility that the price graph of an actual stock could be sufficiently deterministic for various prediction goals but appear random to all polynomial-time prediction algorithms.

cs.CE↗

arXiv2000

Triality of Four Dimensional Strings and Networks

We apply the string-triality\cite{duffetal} to argue the existence of the string-networks of solitonic T and U-strings in the heterotic theory on T^6, S and T-strings in IIB on K3 x T^2 and, S and U-strings in IIA on K3 x T^2. We then show the existence of the above heterotic string networks by analyzing the supersymmetry property of the supergravity solutions. The consistency of these networks with supersymmetry in the case of IIA and IIB theories is also argued. Our results therefore give further evidence in favor of the string-triality in four dimensions.

hep-th↗

arXiv2000

On Charged Strings and their Networks

We investigate properties of several string networks in $D < 10$ which carry electric currents as well as electrostatic charge densities. We show the electric-current conservations as well as the force-balance condition of the string tensions on 3-string junctions in these networks. We also show the consistency of the above string networks from their world-volume point of view by comparing the world-volume energy-density with the induced worldsheet energy density of the supergravity solution. Finally, we present new charged macroscopic string solutions in type II theories in D=8 and discuss certain issues related to their network construction.

hep-th↗

arXiv2000

Non-Planar String Networks on Tori

Type II strings in D=5 contain particle-like 1/8 supersymmetric BPS states. In this note we give a string-network representation of such states by considering (periodic) non-planar $(p,q,r)$-string networks of eight dimensional type II string theory on $T^3$. We obtain the BPS mass formula of such states, in terms of charges and generating-vectors of the torus, and show its invariance under an $SL(3, Z)\times SL(3, Z)$ group of transformations. Results are then generalized to string-networks associated with the $SL(5, Z)$ $U$-duality in seven dimensions. We also discuss reinterpretation of the above $(D=5)$ mass formula in terms of BPS states in world-volume theories of $U2$-branes in D=8.

hep-th↗

arXiv1999

Charged Macroscopic type II Strings and their Networks

We write down charged macroscopic string solutions in type II string theories, compactified on torii, and present an explicit solution of the spinor Killing equations to show that they preserve 1/2 of the type II supersymmetries. The S-duality symmetry of the type IIB string theory in ten-dimensions is used to write down the SL(2,Z) multiplets of such strings and the corresponding 1/2 supersymmetry conditions. Finally we present examples of planar string networks, using charged macroscopic (p,q)-strings. An interesting feature of some of these networks, which preserve 1/4 supersymmetry, is a required alignment among three parameters, namely the orientation of strings, a U(1) phase associated with the maximal compact subgroup of SL(2, Z), and an (angular) parameter associated with a solution generating transformation, which is responsible for creating charges and currents on the strings.

hep-th↗

arXiv1999

A Note on Orientifolds and Dualities of Type 0B String Theory

We generalize the construction of four dimensional non-tachyonic orientifolds of type 0B string theory to non-supersymmetric backgrounds. We construct a four dimensional model containing self-dual D3 and D9-branes and leading to a chiral anomaly-free massless spectrum. Moreover, we discuss a further tachyon-free six dimensional model with only D5 branes. Eventually, we speculate about strong coupling dual models of the ten-dimensional orientifolds of type 0B.

hep-th↗

arXiv1999

String Multiplets from an Invariant 2-Brane

We study a three-dimensional gauge theory obtained from the dimensional reduction of a D4-brane worldvolume theory in the background of space-time moduli. An SL(3) symmetry in this theory, which acts on fields as well as coupling constants, is identified. By comparing the energies with the string tensions, we show that certain 1/2 supersymmetric classical solutions of this theory can be identified as SL(3,Z) multiplets of type II strings in eight dimensions. Results are then generalized to the non-linear Born-Infeld action. We also discuss the possibility of 1/8 BPS states in this theory and their representations in terms of string networks.

hep-th↗

arXiv1998

U-duality and Network Configurations of Branes

We explicitly write down the invariant supersymmetry conditions for branes with generic values of moduli and U-duality charges in various space-time dimensions $D \leq 10$. We then use these results to obtain new BPS states, corresponding to network type structure of such branes.

hep-th↗

arXiv1998

String Network and U-Duality

We discuss the generalization of recently discovered BPS configurations, corresponding to the planar string networks, to non-planar ones by considering the U-duality symmetry of type II string theory in various dimensions. As an explicit example, we analyze the string solutions in 8-dimensional space-time, carrying SL(3) charges, and show that by aligning the strings along various directions appropriately, one can obtain a string network which preserves 1/8 supersymmetry.

hep-th↗

arXiv1997

Oscillating D-Strings from IIB Matrix Theory

We present a class of BPS solutions of the IIB Matrix Theory which preserve 1/4 supersymmetry. The solutions desrcibe D-string configurations with left-moving oscillations. We demonstrate that the one-loop quantum effective action of Matrix Theory vanishes for this solution, confirming its BPS nature. We also study the world-volume gauge theory of oscillating strings and show its connection with static D-strings.

hep-th↗

arXiv1997

BPS States in N=3 Superstrings

The N = 3 string models are special solutions of the type II perturbative string theories. We present explicit expressions for the helicity supertraces,which count the number of the perturbative BPS multiplets. Assuming the non-perturbative duality $(S\leftrightarrow T)$ of the heterotic string on T^6 and type II on K_3 x T^2 valid in N = 4 theories, we derive the N = 3 non-perturbative BPS mass formula by "switching off" some of the N = 4 charges and "fixing" to special values some of the N = 4 moduli. This operation corresponds to a well-defined Z_2 projection acting freely on the compactification manifold. The consistency of this projection and the precise connection of the N = 4 and N = 3 BPS spectrum is shown explicitly in several type II string constructions. The heterotic N = 3 and some asymmetric type II constructions turn out to be non-perturbative with the S moduli fixed at the self-dual point S=i. Some of the non-perturbative N = 3 type II are defined in the context of F-theory. The bosonic sector of the N=3 string effective action is also presented. This part can be useful for the study of 4d black holes in connection with the asymptotic density of BPS states in N = 3 string theory.

hep-th↗

arXiv1997

U-Manifolds

We use non-perturbative U-duality symmetries of type II strings to construct new vacuum solutions. In some ways this generalizes the F-theory vacuum constructions. We find the possibilities of new vacuum constructions are very limited. Among them we construct new theories with N=2 supersymmetry in 3-dimensions and (1, 1) supersymmetry in 2-dimensions.

hep-th↗

arXiv1996

Compactification of $M$-Theory to Two Dimensions

Compactifications of M-theory to two dimensional space-time on ${(K3\times \T^5)}/ \Z_2$ and ${(K3\times K3\times §^1)}/ \Z_2$ orientifolds are presented. These orientifolds provide examples of anomaly free chiral supergravity models in two dimensions with (8, 0) and (4, 0) supersymmetries. Anomaly free spectra at the enhanced symmetry points are also obtained. The results confirm the twisted sector contribution to the spectrum in the case of $\T^9/ \Z_2$ discussed earlier.

hep-th↗

arXiv1996

M-Theory on Orientifolds of $K_3 \times S^1$

We present several Orientifolds of M-Theory on $K_3\times S^1$ by additional projections with respect to the finite abelian automorphism groups of $K_3$. The resulting models correspond to anomaly free theories in six dimensions. We construct explicit examples which can be interpreted as models with eight, four, two and one vector multiplets and $N=1$ supersymmetry in six dimensions.

hep-th↗

arXiv1996

K-Models and Type IIB Superstring Backgrounds

A family of type IIB superstring backgrounds involving Ramond-Ramond fields are obtained in ten dimensions starting from a K-model through a generalization of our recent results. The unbroken global $SL(2,R)$ symmetry of the type IIB equations of motion are implemented in this context as a solution generating transfromation. A geometrical analysis, based on the tensor structure of the higher order $α^{\prime}$ terms in the equations of motion, is employed to show that these backgrounds are exact.

hep-th↗

arXiv1996

Exact Type IIB Superstring Backgrounds

We obtain a family of type IIB superstring backgrounds involving Ramond-Ramond fields in ten dimensions starting from a heterotic string background with vanishing gauge fields. To this end the global $SL(2,R)$ symmetry of the type IIB equations of motion is implemented as a solution generating transformation. Using a geometrical analysis we show that the type IIB backgrounds obtained are solutions to all orders in $α^{\prime}$.

hep-th↗

arXiv1996

Orientifold and Type II Dual Pairs

In this paper we present a symmetry of a toroidally compactified type II string theory. This symmetry has the interpretaion that it interchanges the left and the right-moving worldsheet coordinates and reverses the orientations of some of the spatial coordinates. We also identify another discrete symmetry of the type II theory which is related to the above one by a nontrivial U-duality element of string theory. This symmetry, however, has trivial action on the worldsheet coordinates and corresponds to an improper T-duality rotation. We then construct examples of type II dual pairs in four dimensions by modding out the known type II dual pairs by the above symmetries. We show the explicit matching of the spectrum and supersymmetries in these examples.

hep-th↗

arXiv1995

Ehlers Transformations and String Effective Action

We explicitly obtain the generalization of the Ehlers transformation for stationary axisymmetric Einstein equations to string theory. This is accomplished by finding the twist potential corresponding to the moduli fields in the effective two dimensional theory. Twist potential and symmetric moduli are shown to transform under an $O(d,d)$ which is a manifest symmetry of the equations of motion. The non-trivial action of this $O(d,d)$ is given by the Ehlers transformation and belongs to the set $O(d) \times O(d)\over O(d) $.

hep-th↗