arXiv subjects

Mohammad R. Garousi

Publications and source records attributed to Mohammad R. Garousi.

At least 55 records · Page 3Linked to original sources

arXiv2020

Minimal gauge invariant couplings at order $α'^3$: NS-NS fields

Removing the field redefinitions, the Bianchi identities and the total derivative freedoms from the general form of gauge invariant NS-NS couplings at order $α'^3$, we have found that the minimum number of independent couplings is 872. We find that there are schemes in which there is no term with structures $R,\,R_{μν},\,\nabla_μH^{μαβ}$, $ \nabla_μ\nabla^μΦ$. In these schemes, there are sub-schemes in which, except one term, the couplings can have no term with more than two derivatives. In the sub-scheme that we have chosen, the 872 couplings appear in 55 different structures. We fix some of the parameters in type II supersting theory by its corresponding four-point functions. The coupling which has term with more than two derivatives is constraint to be zero by the four-point functions.

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arXiv2020

T-duality constraint on R-R couplings

It has been speculated that the metric, $B$-field and dilaton couplings in the low energy effective action of string theory at any order of $α'$ may be found by imposing the gauge symmetries and the T-duality on the effective action. This proposal can be extended to include the Ramond-Ramond (R-R) couplings as well. In this paper, we first find the dimensional reduction of the R-R fields and then perform explicitly the T-duality constraint on the R-R couplings at the supergravity level. Up to an overall factor, it reproduces the democratic form of the R-R couplings.

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arXiv2020

Surface terms in the effective actions via duality constraints

The effective action of string theory on a spacetime manifold with boundary has both bulk and boundary terms. We propose that both bulk and boundary actions, may be found by imposing the effective action to be invariant under the gauge transformations and under the string dualities. Using this proposal at the leading order of $α'$, the standard Gibbons-Hawking-York boundary term is reproduced.

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arXiv2020

O-plane couplings at order $α'^2$: one R-R field strength

It is known that the anomalous Chern-Simons (CS) coupling of O$_p$-plane is not consistent with the T-duality transformations. Compatibility of this coupling with the T-duality requires the inclusion of couplings involving one R-R field strength. In this paper we find such couplings at order $α'^2$. By requiring the R-R and NS-NS gauge invariances, we first find all independent couplings at order $α'^2$. There are $1,\, 6,\,28,\,20,\, 19,\, 2$ couplings corresponding to the R-R field strengths $F^{(p-4)}$, $\,F^{(p-2)}$, $\,F^{(p)}$, $\,F^{(p+2)}$, $\,F^{(p+4)}$ and $F^{(p+6)}$, respectively. We then impose the T-duality constraint on these couplings and on the CS coupling $C^{(p-3)}\wedge R\wedge R$ at order $α'^2$ to fix their corresponding coefficients. The T-duality constraint fixes all coefficients in terms of the CS coefficient. They are fully consistent with the partial couplings that have been already found in the literature by the S-matrix method.

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arXiv2020

Effective action of bosonic string theory at order $ α'^2 $

Recently, it has been shown that the gauge invariance requires the minimum number of independent couplings for $B$-field, metric and dilaton at order $α'^2$ to be 60. In this paper we fix the corresponding 60 parameters in string theory by requiring the couplings to be invariant under the global T-duality transformations. The Riemann cubed terms are exactly the same as the couplings that have been found by the S-matrix calculations.

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arXiv2019

Four-derivative couplings via T-duality constraint

We examine the proposal that the dimensional reduction of the effective action of perturbative string theory on a circle, should be invariant under T-duality transformations. The T-duality transformations are the standard Buscher rules plus some higher covariant derivatives. By explicit calculations at order $α'$ for metric, dilaton and B-field, we show that the T-duality constraint can fix both the effective action and the higher derivative corrections to the Buscher rules up to an overall factor. The corrections depend on the scheme that one uses for the effective action. We have found the effective action and its corresponding T-duality transformations in an arbitrary scheme.

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arXiv2019

Minimal independent couplings at order $α'^2$

Using field redefinitions and Bianchi identities on the general form of the effective action for metric, $B$-field and dilaton, we have found that the minimum number of independent couplings at order $α'^2$ is 60. We write these couplings in two different schemes in the string frame. In the first scheme, each coupling does not include terms with more than two derivatives and it does not include structures $R,\,R_{μν},\,\nabla_μH^{μαβ}$, $ \nabla_μ\nabla^μΦ$. In this scheme, 20 couplings which are the minimum number of couplings for metric and $B$-field, include dilaton trivially as the overall factor of $e^{-2Φ}$, and all other couplings include derivatives of dilaton. In the second scheme, the dilaton appears in all 60 coupling only as the overall factor of $e^{-2Φ}$. In this scheme, 20 of the couplings are exactly the same as those in the previous scheme.

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arXiv2018

$O(D,D)$-constraint on $D$-dimensional effective actions

Double Field Theory is a manifestly T-duality invariant formulation of string theory in which the effective theory at any order of $α'$ is invariant under global $O(D,D)$ transformations and ought to be invariant under gauge transformations which receive $α'$-corrections. On the other hand, the effective theory in the usual $D$-dimensional formulation of string theory is manifestly gauge invariant and ought to be invariant under T-duality transformations which receive $α'$-corrections. We speculate that the combination of these two constraints may fix both the $2D$-dimensional and the $D$-dimensional effective actions without knowledge of the $α'$-corrections of the gauge and the T-duality transformations. In this paper, using generalized fluxes, we construct arbitrary $O(D,D)$-invariant actions at orders $α'^0$ and $α'$, and then dimensionally reduce them to the $D$-dimensional spacetime. On the other hand, at these orders, we construct arbitrary covariant $D$-dimensional actions. Constraining the two $D$-dimensional actions to be equal up to non-covariant field redefinitions, we find that both actions are fixed up to overall factors and up to field redefinitions.

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arXiv2018

$R^4 $ terms in supergravities via T-duality constraint

It has been speculated in the literature that the effective actions of string theories at any order of $α'$ should be invariant under the Buscher rules plus their higher covariant derivative corrections. This may be used as a constraint to find effective actions at any order of $α'$, in particular, the metric, the B-field and the dilaton couplings in supergravities at order $α'^3$ up to an overall factor. For the simple case of zero B-field and diagonal metric in which we have done the calculations explicitly, we have found that the constraint fixes almost all the seven independent Riemann curvature couplings. There is only one term which is not fixed, because when metric is diagonal, the reduction of two $R^4$ terms become identical. The Riemann curvature couplings that the T-duality constraint produces for both type II and Heterotic theories are fully consistent with the existing couplings in the literature which have been found by the S-matrix and by the sigma-model approaches.

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arXiv2018

T-duality invariant effective actions at orders $ α', α'^2$

We use compatibility of the $D$-dimensional effective actions for diagonal metric and for dilaton with the T-duality when theory is compactified on a circle, to find the the $D$-dimensional couplings of curvatures and dilaton as well as the higher derivative corrections to the $(D-1)$-dimensional Buscher rules at orders $ α' $ and $α'^2$. We observe that the T-duality constraint on the effective actions fixes the covariant effective actions at each order of $α'$ up to field redefinitions and up to an overall factor. Inspired by these results, we speculate that the $D$-dimensional effective actions at any order of $α'$ must be consistent with the standard Buscher rules provided that one uses covariant field redefinitions in the corresponding reduced $(D-1)$-dimensional effective actions. This constraint may be used to find effective actions at all higher orders of $α'$.

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arXiv2017

S-matrix element of two R-R and one NS states

We explicitly calculate the disk-level S-matrix element of two closed string R-R and one open string NS vertex operators in RNS formalism. We show that the amplitude satisfies various duality Ward identities. In particular, when one of the R-R is zero-form, the other one is two-form and the NS state is gauge boson, the amplitude transforms under S-duality Ward identity to the amplitude of one dilaton, one B-field and one gauge boson which has been recently calculated explicitly. We have also proposed a soft theorem for disk-level scattering amplitude of arbitrary number of hard closed strings and one soft open string at the leading order of soft momentum, and shown that the above amplitude satisfies the soft theorem.

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arXiv2017

Duality constraints on effective actions

Superstring theories at low energy limit are described by the corresponding supergravities, and their non-perturbative D-brane/O-plane excitations are described by DBI and WZ actions. Higher derivative corrections to these effective actions are important for understanding the stringy behavior of the fundamental objects. They may be extracted from the contact terms of the corresponding S-matrix elements. On the other hand, the superstring theories enjoy the T- and S-dualities which appear in the S-matrix elements as duality Ward identities. These Ward identities might be used as generating functions for constructing the S-matrix elements. The dualities may also be used directly to construct the effective actions. In this article, we review the duality Ward identities which can be used to generate S-matrix elements, and review the dualities which may be used directly to construct the higher derivative corrections to the effective actions.

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arXiv2016

Higher derivative corrections to WZ action: One RR, one NSNS and one NS couplings

In the first part of this paper, we calculate the disk-level S-matrix elements of one RR, one NSNS and one NS vertex operators, and show that they are consistent with the amplitudes that have been recently found by applying various Ward identities. We show that the massless poles of the amplitude at low energy are fully consistent with the known D-brane couplings at order $α'^2$ which involve one RR or NSNS and two NS fields. Subtracting the massless poles, we then find the contact terms of one RR, one NSNS and one NS fields at order $α'^2$. Some of these terms are reproduced by the Taylor expansion and the pull-back of two closed string couplings, some other couplings are reproduced by linear graviton in the second fundamental form and by the B-field in the gauge field extension $F\rightarrow F+B$, in one closed and two open string couplings. In the second part, we write all independent covariant contractions of one RR, one NSNS and one NS fields with unknown coefficients. We then constrain the couplings to be consistent with the linear T-duality and with the above contact terms. Interestingly, we have found that up to total derivative terms and Bianchi identities, these constraints uniquely fix all the unknown coefficients.

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arXiv2016

T-duality of $α'$-correction to DBI action at all orders of gauge field

By explicit calculations of four-field couplings, we observe that the higher derivative corrections to the DBI action in flat space-time, can be either in a covariant form or in a T-duality invariant form. The two forms are related by a non-covariant field redefinition. Using this observation, we then propose a non-covariant but T-duality invariant action which includes all orders of massless fields and has two extra derivatives with respect to the DBI action.

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arXiv2016

On T-duality of $R^2$-corrections to DBI action at all orders of gauge field

Recently, it has been observed that in a T-duality invariant world-volume theory in flat spacetime, all orders of gauge field strength and all orders of the D-brane velocity appear in two specific matrices. Using these two matrices, we construct the world-volume couplings of two massless NSNS states at order $α'^2$ and all orders of the velocity and the gauge field strength, by requiring them to be invariant under the linear T-duality. The standard extension $F\rightarrow F+P[B]$, then produces all orders of the pull-back of B-field into the action. We compare the resulting couplings for zero velocity and gauge field strength, with the $α'^2$ terms of the disk-level S-matrix element of two massless NSNS vertex operators in the presence of a constant background B-field. We have found an exact agreement.

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arXiv2016

An off-shell D-brane action at order $ α'^2$ in flat spacetime

We use compatibility of the second fundamental form corrections to DBI action at order $α'^2$ which includes trace of the second fundamental form, with T-duality and with the linear S-duality as guiding principles to find an off-shell D-brane action at order $α'^2$ in type II superstring theories in flat spcetime.

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arXiv2015

On D-brane action at order $ α'^2$

We use compatibility of D-brane action with linear T-duality, S-duality and with S-matrix elements as guiding principles to find all world volume couplings of one massless closed and two open strings at order $α'^2$ in type II superstring theories. In particular, we find that the squares of second fundamental form appear only in world volume curvatures, and confirm the observation that dilaton appears in string frame action via the transformation $\hat{R}_{μν}\rightarrow \hat{R}_{μν}+\nabla_μ\nabla_νΦ$.

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arXiv2015

T-duality of O-plane action at order $ α'^2$

We use compatibility of O-plane action with nonlinear T-duality as a guiding principle to find all NS-NS couplings in the O-plane action at order $α'^2$. We find that the dilaton couplings appear in the string frame only via the transformation $\hat{R}_{μν}\rightarrow \hat{R}_{μν}+\nabla_μ\nabla_νϕ$.

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