arXiv subjects

Mohammad R. Garousi

Publications and source records attributed to Mohammad R. Garousi.

At least 37 records · Page 2Linked to original sources

arXiv2024

T-duality constraint on effective Lagrangians

Recent studies have highlighted the significant role of utilizing $O(1,1)$ symmetry in the circular reduction of effective actions to determine NS-NS couplings in the effective action of string theory. However, these calculations often result in residual terms as total derivatives that do not conform to $O(1,1)$ transformations. In this paper, we present explicit calculations at $α'$ order, demonstrating the enforceability of this symmetry on effective Lagrangians to establish the parameters governing covariant couplings in any scheme. Notably, we discover the $O(1,1)$-invariant Lagrangians corresponding to the Metsaev-Tseytlin action and the Miessner action.

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arXiv2023

More on $β$-symmetry

Recent work has proposed a method for imposing T-duality on the metric, $B$-field, and dilaton of the classical effective action of string theory without using Kaluza-Klein reduction. Specifically, the $D$-dimensional effective action should be invariant under global $O(D,D)$ transformations, provided that the partial derivatives along the $β$-parameters of the non-geometrical elements of the $O(D,D)$ group become zero. In this paper, we speculate that the global $β$-symmetry can be utilized to identify both bulk and boundary couplings. We demonstrate that the Gibbons-Hawking term at the leading order of $α'$ is reproduced by this symmetry. Additionally, for closed spacetime manifolds at order $α'$, we show that the 20 independent geometrical couplings at this order are fixed by this symmetry up to field redefinitions. Specifically, we show that the invariance of the most general covariant and gauge invariant bulk action at order $α'$ under the most general covariant deformed $β$-transformation at order $α'$ fixes the action up to 13 parameters. These parameters reflect the field redefinitions freedom for the closed spacetime manifolds. For particular values of these parameters, we recover the effective action in the Metsaev-Tseytlin and in the Meissner schemes.

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arXiv2023

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

Upon examining the effective action of the heterotic string theory at order $α'^2$, an inconsistency between the Chern-Simons coupling $Ω^2$ and T-duality has been discovered. To address this issue, we introduce 60 parity-even independent geometrical couplings involving the $B$-field, metric, and dilation at the same order, each with arbitrary coefficients. To ensure the invariance of these couplings under T-duality, we consider the Miessner action for the couplings at order $α'$ and rigorously determine the coefficients of the 60 couplings in terms of the Chern-Simons coupling. Notably, it is found that the coefficients of the Riemann cubed terms must be zero, which aligns with the results of S-matrix calculations. Additionally, the parity odd couplings at order $α'^2$ are obtained through T-duality. Overall, our analysis successfully resolves the inconsistency between the Chern-Simons coupling and T-duality, providing a more comprehensive understanding of the behavior of the heterotic string theory at order $α'^2$.

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arXiv2023

Exploring $β$-symmetry in heterotic theory at order $α'$ with boundary term

This paper investigates the $β$-symmetry of the heterotic string theory at order $α'$ in the context of open spacetime manifolds. Our analysis reveals that the parity-odd component of the effective action at this order remains invariant under $β$-transformations. Furthermore, we demonstrate that the corresponding $β$-transformations leave the Gibbons-Hawking boundary term invariant.

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arXiv2023

The data on the boundary at order $α'$

The least action principle indicates that for the open spacetime manifolds, there are data on the boundary. Recently, it has been proposed that the data for the effective actions at order $α'$ are the values of the massless fields and their first derivatives. These data should be respected by the T-duality transformations at order $α'$. Moreover, the T-duality transformations should not change the unit vector to the boundary which in turns implies that the base space metric should be also invariant. Assuming such restricted T-duality transformations, we show that the transformation of the circular reduction of the parity-odd part of the effective action of the heterotic string theory at order $α'$ under the Buscher rules is cancelled by some total derivative terms and by some restricted T-duality transformations at order $α'$. Using the Stokes' theorem, we then show that the boundary terms in the base space corresponding to the total derivative terms are $exactly$ cancelled by transformation of the circular reduction of the Gibbons-Hawking boundary term under the above restricted T-duality transformations. These calculations confirm the above proposal for the data on the boundary for the effective actions at order $α'$.

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arXiv2023

Higher-derivative couplings and torsional Riemann curvature

Using the most general higher-derivative field redefinition for the closed spacetime manifolds, we show that the tree-level couplings of the metric, $B$-field and dilaton at orders $α'^2$ and $α'^3$ that have been recently found by the T-duality, can be written in a particular scheme in terms of the torsional Riemann curvature ${\cal R}$ and the torsion tensor $H$. The couplings at order $α'^2$ have structures ${\cal R}^3, H^2 {\cal R}^2$, $H^6$, and the couplings at order $α'^3$ have only structures ${\cal R}^4$, $H^2{\cal R}^3$. Replacing ${\cal R}$ with the ordinary Riemann curvature, the couplings in the structure $H^2{\cal R}^3$ reproduce the couplings found in the literature by the S-matrix method.

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arXiv2022

T-duality of D-brane versus O-plane actions

It is known that, in the static gauge, the world-volume and the transverse Kaluza-Klein (KK) reductions of the O-plane effective actions on a circle satisfy the T-duality constraint for arbitrary base space background. In this paper we show that due to the presence of the second fundamental form in the D-brane couplings at order $α'$ and higher, the T-duality is satisfied only for a subclass of couplings for arbitrary base space background. They are $m=0$ couplings where $m$ is the number of $\tilde{B}$-field (without derivative on it). For $m>0$ couplings, the base space metric must be block-diagonal and the momentum $U(1)$ vector field must be zero. However, the derivatives of the metric and the vector field are arbitrary. Using the assumption that the effective actions at the critical dimension are background independent, we then show that the T-duality constraint for the couplings at order $α'$ and for $m=0$, fixes completely both bulk and boundary actions. These couplings indicate that the propagators of the massless open string fields receive $α'$-correction. We have also imposed the T-duality constraint on $m=1,2,3,4$ couplings. Because of the above restriction on the base space background in these cases, however, the T-duality can only partially fix the couplings for $m>0$. This study shows that the Dirac-Born-Infeld (DBI) factor appears in both bulk and boundary actions at order $α'$.

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arXiv2022

Couplings of order six in the gauge field strength and the second fundamental form on a D$_p$-brane at order $α'^2$

Using the assumption that the independent gauge invariant couplings on the world-volume of the non-perturbative objects in the string theory are independent of the background, we find the four and the six gauge field strength and/or the second fundamental form couplings on the world volume of a D$_p$-brane in the superstring theory at order $α'^2$ in the normalization that $F$ is dimensionless. We have found them by considering the particular background which has one circle and by imposing the corresponding T-duality constraint on the independent couplings. In particular, we find that there are 12+146 independent gauge invariant couplings at this order, and the T-duality constraint can fix 150 of them. We show that these couplings are fully consistent with the partial results in the literature. This comparison also fixes the remaining 8 couplings.

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arXiv2022

Higher-derivative field redefinitions in the presence of boundary

Recently it has been proposed that the consistency with T-duality requires the effective action of string theory at order $α'^n$ satisfies the least action principle provided that the values of the massless fields and their derivatives up to order $n$ are known on the boundary. In this paper we speculate that this boundary condition constrains the field redefinitions and the corrections to the T-duality transformations in the presence of boundary, \eg at order $α'$, the metric does not change, and all other massless fields should change to include only the first derivative of the massless fields. Using the above field redefinitions, we write all gauge invariant bulk and boundary couplings in the bosonic string theory at order $α'$ in a minimal scheme. Then using the assumption that the classical effective action of the string theory at the critical dimension is background independent, we fix the coefficients of the independent gauge invariant couplings by imposing $O(1,1)$ symmetry when the background has a circle and by imposing $O(d,d)$ symmetry when the background has $T^d$. These constraints fix the bulk action up to an overall factor, and the boundary action up to two parameters. By requiring the gravity couplings in the boundary action to be consistent with those in the Chern-Simons gravity, the two boundary parameters are also fixed. Up to the above restricted field redefinitions, the bulk and boundary couplings are exactly those in the K.A. Meissner action and its corresponding boundary action.

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arXiv2022

Background independence of effective actions at critical dimension

Recently, by explicit calculations at orders $α',α'^2,α'^3$, it has been observed that the effective action of string theory at the critical dimension is independent of the background for the closed spacetime manifolds. In this paper we speculate that for the open spacetime manifolds, the effective action is even independent of the character of the boundary, \ie the boundary couplings for timelike and spacelike boundaries are the same. We support this proposal by calculating the boundary couplings in the bosonic string theory at order $α'$ for the spacelike boundary and show that they are the same as the couplings for the timelike boundary that have been recently found.

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arXiv2022

Minimal gauge invariant couplings at order $\ell_p^6$ in M-theory

Removing the field redefinitions, the Bianchi identities and the total derivative freedoms from the general form of the gauge invariant couplings at order $\ell_p^6$ for the bosonic fields of M-theory, we have found that the minimum number of independent couplings in the structures with even number of the three-form, is 1062. We find that there are schemes in which there is no coupling involving $R,\,R_{μν},\,\nabla_μF^{μαβγ}$. In these schemes, there are sub-schemes in which, except one coupling which has the second derivative of $F^{(4)}$, the couplings can have no term with more than two derivatives. We find some of the parameters by dimensionally reducing the couplings on a circle and comparing them with the known couplings of the one-loop effective action of type IIA superstring theory. In particular, we find the coupling which has term with more than two derivatives is zero.

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arXiv2021

Effective action of string theory at order $α'$ in the presence of boundary

Recently, using the assumption that the string theory effective action at the critical dimension is background independent, the classical on-shell effective action of the bosonic string theory at order $α'$ in a spacetime manifold without boundary has been reproduced, up to an overall parameter, by imposing the $O(1,1)$ symmetry when the background has a circle. In the presence of the boundary, we consider a background which has boundary and a circle such that the unit normal vector of the boundary is independent of the circle. Then the $O(1,1)$ symmetry can fix the bulk action without using the lowest order equation of motion. Moreover, the above constraints and the constraint from the principle of the least action in the presence of boundary can fix the boundary action, up to five boundary parameters. In the least action principle, we assume that not only the values of the massless fields but also the values of their first derivatives are arbitrary on the boundary. We have also observed that the cosmological/one-dimensional reduction of the leading order action in the presence of the Hawking-Gibbons boundary term, produces zero boundary action. Imposing this as another constraint on the boundary couplings at order $α'$, we find the boundary action up to two parameters. For a specific value for these two parameters, the gravity couplings in the boundary become the Chern-Simons gravity plus another term which has the Laplacian of the extrinsic curvature.

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arXiv2021

On NS-NS couplings at order $α'^3$

Recently, imposing the gauge-symmetry and the T-duality constraints on the string frame effective actions of type II superstring theories, the NS-NS cuplings have been found in a particular scheme which has 445 couplings in 15 different structures. In this paper, using a field redefinition, we write them in terms of 251 couplings which appear in 9 different structures. The 9 structures involve only Riemann curvature, $H_{αβμ}$ and $\nabla_αH_{βμν}$. The number of couplings in the structures $R^4$, $H^8$, $H^6R$, $H^4R^2$, $H^2R^3$ are $2,\, 2,\, 1,\, 7,\,22$, respectively, and the number of couplings in the structures $(\nabla H)^4$, $(\nabla H)^2 R^2$, $(\nabla H)^2 H^4$, $(\nabla H)^2H^2R$ are $12,\, 22,\, 77,\, 106$, respectively. The new couplings are fully consistent with the sphere-level S-matrix element of four NS-NS vertex operators.

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arXiv2021

$O(25,25)$ symmetry of bosonic string theory at order $α'^2$

It has been recently observed that the imposition of the $O(1,1)$ symmetry on the circle reduction of the classical effective action of string theory, can fix the effective action of the bosonic string theory at order $α'^2$, up to an overall factor. In this paper, we use the cosmological reduction on the action and show that, up to one-dimensional field redefinitions and total derivative terms, it can be written in the $O(25,25)$-invariant form proposed by Hohm and Zwiebach.

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arXiv2021

$O(9,9)$ symmetry of NS-NS couplings at order $α'^3$

Recently, imposing the $O(1,1)$ symmetry on the circle reduction of the classical effective action of string theory, we have found all NS-NS couplings of type II superstring theories at order $α'^3$. In this paper we use the cosmological reduction on the couplings and show that, up to field redefinitions and total derivative terms, they are invariant under the $O(9,9)$ transformations.

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arXiv2021

$α'$-corrections to DBI action via T-duality constraint

It is known that D$_p$-brane effective action at the leading order of $α'$ in flat space-time which is given by DBI action, transforms to D$_{p-1}$-brane effective action under standard T-duality transformations of the open string gauge bosons and transverse scalar fields. Extending this duality to order $α'$, one may find corrections to the DBI action which include the second fundamental form $Ω$ and the covariant derivative of gauge field strength $DF$, as well as the corrections to the T-duality transformations. Using this idea, up to two parameters, we have found all 81 covariant couplings of $D FD F$ and $ΩΩ$ with zero, two, four and six $F$'s. The four gauge field couplings that the T-duality constraint fixes are consistent with the known couplings in the literature.

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arXiv2021

Surface terms in effective action of O-plane at order $α'^2$

The effective action of string theory has both bulk and boundary terms if the spacetime is an open manifold. Recently, the known classical effective action of string theory at the leading order of $α'$ and its corresponding boundary action have been reproduced by constraining the effective actions to be invariant under gauge transformations and under string duality transformations. In this paper, we use this idea to find the classical effective action of the O-plane and its corresponding boundary terms in type II superstring theories at order $α'^2$ and for NS-NS couplings. We find that these constraints fix the bulk action and its corresponding boundary terms up to one overall factor. They also produce three multiplets in the boundary action that their coefficients are independent of the bulk couplings under the string dualities.

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arXiv2021

Effective action of type II superstring theories at order $α'^3$: NS-NS couplings

Recently, it has been shown that the minimum number of gauge invariant couplings for $B$-field, metric and dilaton at order $α'^3$ is 872. These couplings, in a particular scheme, appear in 55 different structures. In this paper, up to an overall factor, we fix all parameters in type II supertirng theories by requiring the reduction of the couplings on a circle to be invariant under T-duality transformations. We find that there are 445 non-zero couplings which appear in 15 different structures. The couplings are fully consistent with the partial couplings that have been found in the literature by the four-point S-matrix element and by the non-linear Sigma model methods.

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