Zero-slope Limit Research Articles

Hall–Petch strengthening limit through partially active segregation in nanocrystalline Ag-Cu alloys

The breakdown from grain-size strengthening to softening mechanisms is generally well understood for high-purity nanocrystalline materials when the mean grain size decreases to the nanometer range. In nanocrystalline alloys, however, the stabilization of nanosized grains by grain-boundary solute segregation complicates the above mechanisms. Moreover, current segregation models have little predictive power for determining the optimal solute content that maximizes Hall-Petch strengthening effects. In this article, using large-scale hybrid Monte-Carlo/molecular dynamic simulations, we present a systematic study of the Hall–Petch breakdown in Cu-segregated Ag alloys with grain sizes ranging from 8 nm to 59 nm, where three concentration-dependent regimes of plasticity are described: (1) Classical segregation strengthening behavior at low solute contents, (2) shear band-induced softening at high solute contents, and (3) a previously unknown, but extended plateau of maximum strengths for intermediate solute contents from 4 to 15 at.%, which we term as nanocrystalline Sterling silver. We find that flow strengths in nanocrystalline Sterling alloys naturally exhibit a zero-slope limit at the smallest grain sizes that is well below the ideal Hall–Petch strengthening trend. This phenomenon results from partially active grain-boundary segregation that acts to influence interfacial plasticity in some, but not all, grain boundary regions. Our findings amplify the atomic nature of solute segregation and interaction at grain boundaries and its complex roles on grain boundary-mediated plasticity mechanisms in nanocrystalline alloys.

Four-gauge-particle scattering amplitudes and Polyakov string path integral in the proper-time gauge

We evaluate four-gauge-particle tree level scattering amplitudes using the Polyakov string path integral in the proper-time gauge, where the string path integral can be cast into the Feynman-Schwinger proper-time representation. We compare the resultant scattering amplitudes, which include α′-corrections, with the conventional ones that may be obtained by substituting local vertex operators for the external string states. In the zero-slope limit, both amplitudes are reduced to the four-gauge-particle scattering amplitude of non-Abelian Yang-Mills gauge theory. However, when the string corrections become relevant with finite α′, the scattering amplitude in the proper-time gauge differs from the conventional one: The Polyakov string path integral in the proper-time gauge, equivalent to the deformed cubic string field theory, systematically provides the alpha prime corrections. In addition, we find that the scattering amplitude in the proper-time gauge contains tachyon poles in a manner consistent with three-particle-scattering amplitudes. The scattering amplitudes evaluated using the Polyakov string path integral in the proper-time gauge may be more suitable than conventional ones for exploring string corrections to the quantum field theories and high energy behaviors of open string.

Covariant open string field theory on multiple Dp-branes**Supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2017R1D1A1A02017805)

We study covariant open bosonic string field theories on multiple Dp-branes by using the deformed cubic string field theory, which is equivalent to string field theory in the proper-time gauge. Constructing the Fock space representations of the three-string vertex and the four-string vertex on multiple Dp-branes, we obtain the field theoretical effective action in the zero-slope limit. On multiple D0-branes, the effective action reduces to the Banks-Fishler-Shenker-Susskind (BFSS) matrix model. We also discuss the relation between open string field theory on multiple D-instantons in the zero-slope limit and the Ishibashi-Kawai-Kitazawa-Tsuchiya (IKKT) matrix model. The covariant open string field theory on multiple Dp-branes could be useful to study the non-perturbative properties of quantum field theories in (p + 1)-dimensions in the framework of the string theory. The non-zero-slope corrections may be evaluated systematically by using covariant string field theory.

Covariant open bosonic string field theory on multiple D-branes in the proper-time gauge

We construct a covariant open bosonic string field theory on multiple D-branes, which reduces to a non-Abelian group Yang-Mills gauge theory in the zero-slope limit. Making use of the first quantized open bosonic string in the proper time gauge, we convert the string amplitudes given by the Polyakov path integrals on string world sheets into those of the second quantized theory. The world sheet diagrams generated by the constructed open string field theory are planar in contrast to those of the Witten's cubic string field theory. However, the constructed string field theory is yet equivalent to the Witten's cubic string field theory. Having obtained planar diagrams, we may adopt the light-cone string field theory technique to calculate the multi-string scattering amplitudes with an arbitrary number of external strings. We examine in detail the three-string vertex diagram and the effective four-string vertex diagrams generated perturbatively by the three-string vertex at tree level. In the zero-slope limit, the string scattering amplitudes are identified precisely as those of non-Abelian Yang-Mills gauge theory if the external states are chosen to be massless vector particles.

Deformation of the cubic open string field theory

We study a consistent deformation of the cubic open bosonic string theory in such a way that the non-planar world sheet diagrams of the perturbative string theory are mapped onto their equivalent planar diagrams of the light-cone string field theory with some length parameters fixed. An explicit evaluation of the cubic string vertex in the zero-slope limit yields the correct relationship between the string coupling constant and the Yang–Mills coupling constant. The deformed cubic open string field theory is shown to produce the non-Abelian Yang–Mills action in the zero-slope limit if it is defined on multiple D-branes. Applying the consistent deformation systematically to multi-string world sheet diagrams, we may be able to calculate scattering amplitudes with an arbitrary number of external open strings.

Deformation of Script N = 4 super Yang–Mills theory in graviphoton background

We study deformation of N=4 super Yang-Mills theory from type IIB superstrings with D3-branes in the constant R-R background. We compute disk amplitudes with one graviphoton vertex operator and investigate the zero-slope limit of the amplitudes. We obtain the effective action deformed by the graviphoton background, which contains the one defined in non(anti)commutative N=1 superspace as special case. The bosonic part of the Lagrangian gives the Chern-Simons term coupled with the R-R potential. We study the vacuum configuration of the deformed Lagrangian and find the fuzzy sphere configuration for scalar fields.

Response of sloping unconfined aquifer to stage changes in adjacent stream. I. Theoretical analysis and derivation of system response functions

We study the interaction of a stream with a sloping unconfined aquifer that the stream is assumed to fully penetrate. The analysis applies to flow in a vertical section, considers the existence of a low-conductivity streambed layer and the flow in the aquifer to be induced by variations of the stream stage. Invoking the Dupuit assumption yields the 1-D Boussinesq equation, extended for a sloping base. The Boussinesq equation is linearised, the derived flow model is critiqued and an objective procedure for determining the linearisation level is developed. We solve the linear governing equation by the method of Laplace transform, with analytical inversion; the horizontal-aquifer case is treated in the zero-slope limit. The system response function is derived for the general case (sloping aquifer, sediment bed layer) and for several specific cases, and solutions are verified against known analytical results. Responses are contrasted for aquifers on positive, negative and zero slopes to step changes in the stage of streams with and without a sediment bed layer. The solutions give the aquifer stage and flow rate, the flow exchange rate at the stream-aquifer interface and the exchanged water volumes (bank storage/release).

The large N limit of C/ZN and supergravity

The /N orbifold of type II string theory has localized tachyons with m2 ranging from −1+1/N to −2/N in units of 2/α'. We show that by restricting attention to the lightest tachyons it is possible to take a zero-slope limit where N is taken to infinity while Nα' is held fixed. This is done by applying Buscher duality in the angular direction of the cone to obtain a supergravity solution on which the tachyons are gravitational instabilities. In this picture, supergravity provides a natural off-shell description of the tachyonic interactions. For example, the three-point couplings can be read off easily (to leading order in 1/N) from the supergravity action, and are in agreement with the on-shell couplings computed using CFT techniques.

Star spectroscopy in the constant B-field background

In this paper we calculate the spectrum of Neumann matrix with zero modes in the presence of the constant B-field in Witten's cubic string field theory. We find both the continuous spectrum inside [−1/3,0) and the constraint on the existence of the discrete spectrum. For generic θ, −1/3 is not in the discrete spectrum but in the continuous spectrum. For each eigenvalue in the continuous spectrum there are four twist-definite degenerate eigenvectors except for −1/3 at which the degeneracy is two. However, for each twist-definite eigenvector the twist parity is opposite among the two spacetime components. Based upon the result at −1/3 we prove that the ratio of brane tension to be one as expected. Furthermore, we discuss the factorization of star algebra in the presence of B-field under the zero-slope limit and comment on the implications of our results to the recent proposed map of Witten's star to Moyal's star.

Closed String Tachyon Condensation on Twisted Circles

We study IIA/B string theory compactified on twisted circles. These models possess closed string tachyons and reduce to type 0B/A theory in a special limit. Using methods of gauged linear sigma models and mirror symmetry we construct a conformal field theory which interpolates between these models and flat space via an auxiliary Liouville direction. Interpreting motion in the Liouville direction as renormalization group flow, we argue that the end point of tachyon condensation in all these models (including 0B/A theory) is supersymmetric type II theory. We also find a zero-slope limit of these models which is best described in a T-dual picture as a type II NS-NS fluxbrane. In this limit tachyon condensation is an interesting and well posed problem in supergravity. We explicitly determine the tachyon as a fluctuation of supergravity fields, and perform a rudimentary numerical analysis of the relevant flows.

Duality rotations and BPS monopoles with space and time noncommutativity

We show that noncommutative electromagnetism and Dirac–Born–Infeld (DBI) theory with scalar fields are SL(2, R) self-dual when noncommutativity is light-like and we are in the slowly varying field approximation. This follows from SL(2, R) self-duality of the commutative DBI Lagrangian and of its zero slope limit that we study in detail. We study a symmetry of noncommutative static configurations that maps space-noncommutativity into space–time (and light-like) noncommutativity. SL(2, R) duality is thus extended to space-noncommutativity. Via Seiberg–Witten map we study the nontrivial action of this symmetry on commutative DBI theory. In particular space–time noncommutative BPS magnetic monopoles corresponds to commutative BPS type magnetic monopoles with both electric and magnetic B-field background. Energy, charge and tension of these configurations are computed and found in agreement with that of a D1-string D3-brane system. We discuss the dual string–brane configuration.

Open N=2 strings in a B-field background and noncommutative self-dual Yang–Mills

In the presence of D-branes, fermionic N=2 strings in 2+2 dimensions can be coupled to a Kähler NS–NS two-form B. We present the corresponding action which produces N=2 supersymmetric boundary conditions and discuss the Seiberg–Witten zero-slope limit. After recalling the constraints on the Chan–Paton gauge group, we demonstrate for U( n) groups that the open N=2 string with a nonzero B-field coincides on tree level with noncommutative self-dual Yang–Mills. Several misconceptions of hep-th/0011206 are corrected.

Two-loop scalar diagrams from string theory

We show how to obtain correctly normalized expressions for the Feynman diagrams of Φ 3 theory with an internal U( N) symmetry group, starting from tachyon amplitudes of the open bosonic string, and suitably performing the zero-slope limit by giving an arbitrary mass m to the tachyon. In particular we present explicit results for the two-loop amplitudes of Φ 3 theory, in preparation for the more interesting case of multiloop amplitudes of non-abelian gauge theories.

Zero-slope limit of the compactified closed bosonic string.

We investigate, in the low-energy limit of the closed bosonic string theory, the role of the toroidal compactification, in which the extra spatial coordinates are circular with radius R. We explicitly show that the double limit \ensuremath{\alpha}'\ensuremath{\rightarrow}0 and R\ensuremath{\rightarrow}0, performed on the tree scattering amplitude of four massless scalar particles, leads to four-dimensional amplitudes describing a diffusion due to the exchange of a scalar, spin-1, and spin-2 particle and that it is not influenced by the compactification procedure adopted.

The one-loop five-graviton scattering amplitude and its low-energy limit

A covariant path-integral calculation of the even-spin structure contribution to the one-loop N-graviton scattering amplitude in the type-II superstring theory is presented. The apparent divergence of the N = 5 amplitude is resolved by separating it into twelve independent terms corresponding to different orders of inserting the graviton vertex operators. Each term is well defined in an appropriate kinematic region and can be analytically continued to physical regions where it develops branch cuts required by unitarity. The zero-slope limit of the N = 5 amplitude is performed, and the Feynman diagram content of the low-energy field theory is examined. Both one-particle irreducible (1PI) and one-particle reducible (1PR) graphs with massless internal states are generated in this limit. One set of 1PI graphs has the same divergent dependence on the cut-off as that found in the four-graviton case, and it is proved that such graphs exist for all N. The 1PR graphs are contributed by the poles in the world-sheet chiral Green functions.

Effective one-loop scalar Lagrangian in no-scale supergravity models.

The total one-loop effective scalar Lagrangian is given in an explicitly field-redefinition-invariant form for a general model with derivative self-couplings of the scalars and scalar couplings to graviton, gauge, and fermion fields. This result is then specialized to no-scale models, with a form of the K\ahler potential that is suggested by the zero-slope limit of superstring theories.

The zero-slope limit of Witten's string field theory with Chan-Paton factors

I demonstrate that open-string field theory with Chan-Paton factors has Yang-Mills theory as its off-shell zero-slope limit. I first add Chan-Paton group factors both to Witten's string field theory and to a non-oriented extension of it. The quadratic and cubic interactions between massless fields are calculated in the zero-slope limit by means of the Neumann functions computed for Witten's theory by Gross and Jevicki and by Cremmer, Schwimmer and Thorn. I show that the only other terms (up to renormalisation) appearing in the zero-slope limit are those from tree-level interactions between four massless fields. These are evaluated off-shell using the conformal mapping and Neumann function techniques developed by Giddings, by Sloan, and by Samuel. The resulting lagrangian is Yang-Mills theory in the Feynman-Lorentz-Baulieu- Thierry-Meig gauge.

Axionic instantons and the creation of expanding universes

Abstract In a class of models of scalar matter coupled to N = 1 supergravity, we investigate the existence of gravitational instantons that correspond to the creation of expanding universes. Expressing the derivatively coupled pseudoscalar field in terms of a second rank antisymmetric tensor field (axion), we show that, under mild assumptions about the scalar potential, the theory possesses axion-induced gravitational instanton solutions with the desired interpretation. The assumptions made can be met in the effective four-dimensional theory obtained in a particular compactification of the zero-slope limit of the ten-dimensional superstring theory. Such a system offers an appealing framework for the natural realization of the recent idea that coupling constants, including the cosmological constant, are determined by universal dynamics.

One-loop amplitudes of closed bosonic strings

We derive the one-loop amplitudes for the emission of tachyons and massless bosons from closed unoriented bosonic strings. Contributions from both the torus and the Klein bottle are included, and the structure of their divergences is discussed. It is shown that in the zero-slope limit, the amplitude for emission of massless bosons agrees with results of point-field calculations for the coupling of scalar fields to gravity. Finally, the possibility of cancelling the leading ultraviolet divergence for a particular gauge group is discussed and illustrated for the vacuum-energy density.

Supersymmetry breaking in superstring-inspired models.

We study one-loop corrections to a four-dimensional field-theory model, including nonperturbative supersymmetry breaking by gaugino condensation, suggested by a particular compactification of the zero-slope limit of a ten-dimensional superstring theory. We find that, unless the vacuum energy is unbounded from below, it vanishes at the minimum of the effective one-loop-corrected potential. If there is a vacuum with broken supersymmetry, it remains degenerate in one direction and the scales of the effective theory are obtained at one loop in terms of only one (discrete) parameter which remains undetermined. One-loop corrections from the effective theory at scales below ${\ensuremath{\Lambda}}_{c}$, where hidden gaugino condensation occurs, generate no soft supersymmetry breaking in the observable sector. The analysis of one-loop effects from scales above ${\ensuremath{\Lambda}}_{c}$ suggests that no soft supersymmetry-breaking terms are generated in the gauge-nonsinglet scalar sector, while if gaugino masses ${\mathit{m}}_{\mathit{g}\mathrm{\ifmmode \tilde{}\else \~{}\fi{}}}$ are generated they are related to the gravitino mass ${\mathit{m}}_{\mathit{g}\mathrm{\ifmmode \tilde{}\else \~{}\fi{}}}$ by ${\mathit{m}}_{\mathit{m}\mathrm{\ifmmode \tilde{}\else \~{}\fi{}}}$=O(1--100)${\mathit{m}}_{\mathit{G}\mathrm{\ifmmode \tilde{}\else \~{}\fi{}}}^{3}$/16${\mathrm{\ensuremath{\pi}}}^{2}$${\mathit{m}}_{\mathit{p}}^{2}$. We discuss possibilities for a viable gauge hierarchy and the generalization of our results to other superstring-inspired models.