arXiv subjects

Theodore G. Erler

Publications and source records attributed to Theodore G. Erler.

5 recordsLinked to original sources

arXiv2005

Integrable Open Spin Chains and the Doubling Trick in N = 2 SYM with Fundamental Matter

We demonstrate that the one-loop anomalous dimension matrix in N = 2 SYM with a single chiral hypermultiplet of fundamental matter, which is dual to AdS_5 X S^5 with a D7-brane filling AdS_5 and wrapped around an $^3 in the S^5, is an integrable open spin chain Hamiltonian. We also use the doubling trick to relate these open spin chains to closed spin chains in pure N = 4 SYM. By using the AdS/CFT correspondence, we find a relation between the corresponding open and closed strings that differs from a simple doubling trick by terms that vanish in the semiclassical limit. We also demonstrate that in some cases the closed string is simpler and easier to study than the corresponding open string, and we speculate on the nature of corrections due to the presence of D-branes that this implies.

hep-th↗

arXiv2004

Locality, Causality, and an Initial Value Formulation for Open String Field Theory

In this paper, we explore the questions of time, locality and causality in the framework of covariant open bosonic string field theory. We show that if an open string field is expressed as a certain local function on spacetime--in particular, a function of the lightcone component of the midpoint and the transverse center of mass degrees of freedom--that cubic string field theory is nonsingular and local in lightcone time. In particular, the theory has a well defined initial value formulation resembling that of an ordinary second order relativistic field theory in lightcone frame. This description can be achieved by a nonsingular unitary transformation on the Fock space, and we demonstrate explicitly that the theory is gauge invariant and the interaction vertex is local in this basis. With an initial value formulation at hand, we are able to construct an explicit second quantized operator formalism for the theory using the Hamiltonian BRST formalism. We also explore issues of causality by considering a singular limit of the theory where all spacetime coordinates are taken to the midpoint. At any stage in this limit, the theory is well-defined and arbitrarily close to being completely local and manifestly causal. We argue that the this limit must account for the macroscopic causality of the string S-matrix.

hep-th↗

arXiv2004

Level Truncation and Rolling the Tachyon in the Lightcone Basis for Open String Field Theory

A recent paper by Gross and Erler (hep-th/0406199) showed that by making a certain well-defined, unitary transformation on the mode basis for the open bosonic string--one that identifies the lightcone component of position with the string midpoint--it is possible to render the action for cubic string field theory local in lightcone time. In this basis, then, cubic string field theory possesses a well-defined initial value formulation and a conserved Hamiltonian. With this new understanding it seems natural to study time dependent solutions representing the the decay of an unstable D-branes. In this paper we study such solutions using level truncation of mode oscillators in the lightcone basis, finding both homogenous solutions by perturbatively expanding the string field in modes $e^{nt}$, and inhomogenous solutions by integrating the equations of motion on a lattice. Truncating the theory to level $(\tilde{2},\tilde{4})$ in $α^+$ oscillators, we find time dependent solutions whose behavior seems to converge to that of earlier solutions constructed in the center of mass basis, where the cubic action contains an infinite number of time derivatives. We further construct time-dependent inhomogeneous solutions including all fields up to level $(\tilde{2},\tilde{4})$. These solutions at the outset display rather erratic behavior due to an unphysical instability introduced by truncating the theory at the linear level. However upon truncating away the field responsible for the instability, we find more reasonable solutions which may possibly represent an approximation to tachyon matter. We conclude with some discussion of future directions.

hep-th↗

arXiv2004

Moyal Formulation of Witten's Star Product in the Fermionic Ghost Sector

In this paper, we recast the fermionic ghost sector of Witten's open bosonic string field theory in the language of noncommutative field theory. In particular, following the methods of hep-th/0202087, we find that in Siegel gauge Witten's star product roughly corresponds to a continuous tensor product of Clifford Algebras, and we formulate important operators of the theory in this language, notably the kinetic operator of vacuum string field theory and the BRST operator describing the vacuum of the unstable D-25 brane. We find that the BRST operator is singular in this formulation. We explore alternative operator/Moyal representations of the star product analogous to the split string description and the discrete Moyal basis developed extensively in recent work by Bars and Matsuo (hep-th/0204260). Finally, we discuss some interesting singularities in the formalism and how they may be regulated.

hep-th↗

arXiv2004

A fresh look at midpoint singularities in the algebra of string fields

In this paper we study the midpoint structure of the algebra of open strings from the standpoint of the operator/Moyal formalism. We construct a split string description for the continuous Moyal product of hep-th/0202087, study the breakdown of associativity in the star algebra, and identify in infinite sequence of new (anti)commutative coordinates for the star product in in the complex plane. We also explain how poles in the open string non(anti)commutativity parameter correspond to certain ``null'' operators which annihilate the vertex, implying that states proportional to such operators tend to have vanishing star product with other string fields. The existence of such poles, we argue, presents an obstruction to realizing a well-defined formulation of the theory in terms of a Moyal product. We also comment on the interesting, but singular, representation $L_0$ which has appeared prominently in the recent studies of Bars {\it et al}.

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