Mass renormalization in string theory: special states

Pius, Roji; Rudra, Arnab; Sen, Ashoke

doi:10.1007/jhep07(2014)058

Cited by 39 publications

(100 citation statements)

References 40 publications

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“…The result depends on the choice of the section, reflecting the fact that the off‐shell amplitudes depend on the choice of local coordinate system around the puncture. However the physical quantities like the renormalized masses and S‐matrix elements are independent of the choice of the section.…”

Section: Off‐shell Amplitudes In the Bosonic String Theorymentioning

confidence: 99%

“…As discussed in , for consistent off‐shell amplitudes we need to impose on the choice of this section the requirement of gluing compatibility. This says that near a boundary of the moduli space when a genus g surface with n ‐punctures degenerates into a genus g 1 surface with n 1 punctures and a genus g 2 surface with n 2 punctures with

g = g_{1} + g_{2}

and

n = n_{1} + n_{2} - 2

, the choice of local coordinates on the original surface must be taken to be those induced from the local coordinates at the punctures on the two surfaces into which it degenerates.…”

Section: Off‐shell Amplitudes In the Bosonic String Theorymentioning

confidence: 99%

“…Thus

| φ_{i} ⟩

actually belongs to the space

H_{1}

described in . By normalizing the basis states

| φ_{i} ⟩

to satisfy

⟨ φ_{i} | c_{0}^{-} c_{0}^{+} | φ_{j} ⟩ = δ_{i j}, c_{0}^{\pm} \equiv \frac{1}{2} (c_{0} \pm {\bar{c}}_{0}),

we can ensure that

⟨ φ_{i}^{c} | b_{0}^{+} b_{0}^{-} | φ_{j}^{c} ⟩ = δ_{i j} .

Thus we can drop the second line of , insert the operator

e^{- s (L_{0} + {\overset{L}{true}}_{0})} e^{i θ (L_{0} - {\overset{L}{true}}_{0})}

in front of

| φ_{i} ⟩

in the first line and set

j = i

in the sum.…”

Section: Off‐shell Amplitudes In the Bosonic String Theorymentioning

confidence: 99%

“…The suggestion made in was to go ahead and compute the renormalized masses and S‐matrix elements using these off‐shell amplitudes despite the latter's dependence on spurious data, and then prove that the renormalized masses and the S‐matrix elements computed this way do not depend on the spurious data. Refs . were able to establish the latter result provided we restrict the choice of local coordinates to within a special class – those satisfying the requirement of gluing compatibility.…”

Section: Introductionmentioning

confidence: 99%

“…We end this introduction with a word on convention. As emphasized in , an off‐shell amplitude

Γ_{a_{1} \dots a_{n}}^{(n)} (k_{1}, \dots k_{n})

in string theory – where

a_{i}

denotes the quantum numbers and

k_{i}

denotes the momentum of the i ‐th external state – do not compute the analog of the off‐shell Green's function

G_{a_{1} \dots a_{n}}^{(n)} (k_{1}, \dots k_{n})

in a quantum field theory. Instead the two are related as

Γ_{a_{1} \dots a_{n}}^{(n)} (k_{1}, \dots k_{n}) = G_{a_{1} \dots a_{n}}^{(n)} (k_{1}, \dots k_{n}) \prod_{i = 1}^{n} (k_{i}^{2} + m_{i}^{2})

where

m_{i}

is the tree level mass of the i ‐th external state.…”

Section: Introductionmentioning

confidence: 99%

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Off-shell Amplitudes in Superstring Theory

Sen

2015

Fortschr. Phys.

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176

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Computing the renormalized masses and S-matrix elements in string theory, involving states whose masses are not protected from quantum corrections, requires defining off-shell amplitude with certain factorization properties. While in the bosonic string theory one can in principle construct such an amplitude from string field theory, there is no fully consistent field theory for type II and heterotic string theory. In this paper we give a practical construction of off-shell amplitudes satisfying the desired factorization property using the formalism of picture changing operators. We describe a systematic procedure for dealing with the spurious singularities of the integration measure that we encounter in superstring perturbation theory. This procedure is also useful for computing on-shell amplitudes, as we demonstrate by computing the effect of Fayet-Iliopoulos D-terms in four dimensional heterotic string theory compactifications using this formalism.Comment: LaTeX file, 79 pages, 14 figures; v2 references and clarifications added, normalisation fixed to facilitate construction of 1PI string field theory, notations simplified; v3: minor changes; v4: minor additions and typos correcte

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Section: Off‐shell Amplitudes In the Bosonic String Theorymentioning

confidence: 99%

g = g_{1} + g_{2}

and

n = n_{1} + n_{2} - 2

, the choice of local coordinates on the original surface must be taken to be those induced from the local coordinates at the punctures on the two surfaces into which it degenerates.…”

Section: Off‐shell Amplitudes In the Bosonic String Theorymentioning

confidence: 99%

“…Thus

| φ_{i} ⟩

actually belongs to the space

H_{1}

described in . By normalizing the basis states

| φ_{i} ⟩

to satisfy

⟨ φ_{i} | c_{0}^{-} c_{0}^{+} | φ_{j} ⟩ = δ_{i j}, c_{0}^{\pm} \equiv \frac{1}{2} (c_{0} \pm {\bar{c}}_{0}),

we can ensure that

⟨ φ_{i}^{c} | b_{0}^{+} b_{0}^{-} | φ_{j}^{c} ⟩ = δ_{i j} .

Thus we can drop the second line of , insert the operator

e^{- s (L_{0} + {\overset{L}{true}}_{0})} e^{i θ (L_{0} - {\overset{L}{true}}_{0})}

in front of

| φ_{i} ⟩

in the first line and set

j = i

in the sum.…”

Section: Off‐shell Amplitudes In the Bosonic String Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…We end this introduction with a word on convention. As emphasized in , an off‐shell amplitude

Γ_{a_{1} \dots a_{n}}^{(n)} (k_{1}, \dots k_{n})

in string theory – where

a_{i}

denotes the quantum numbers and

k_{i}

denotes the momentum of the i ‐th external state – do not compute the analog of the off‐shell Green's function

G_{a_{1} \dots a_{n}}^{(n)} (k_{1}, \dots k_{n})

in a quantum field theory. Instead the two are related as

Γ_{a_{1} \dots a_{n}}^{(n)} (k_{1}, \dots k_{n}) = G_{a_{1} \dots a_{n}}^{(n)} (k_{1}, \dots k_{n}) \prod_{i = 1}^{n} (k_{i}^{2} + m_{i}^{2})

where

m_{i}

is the tree level mass of the i ‐th external state.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Off-shell Amplitudes in Superstring Theory

Sen

2015

Fortschr. Phys.

Self Cite

176

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Off‐Shell Amplitudes in String Theory and Hyperbolic Geometry

Moosavian

Pius

2020

Fortschritte der Physik

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The construction of off‐shell amplitudes in closed string theory using Riemann surfaces having constant curvature −1 is explored in detail. Off‐shell string amplitudes constructed using surfaces with constant curvature −1 fail to satisfy the off‐shell factorization properties, and as a result, scattering amplitudes computed using them are ill‐defined. In this paper, we describe a procedure for systematically modifying this construction and obtain consistent off‐shell amplitudes in closed string theory satisfying the off‐shell factorization properties.

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Introduction

Erbin

2021

Lecture Notes in Physics

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Mass renormalization in string theory: special states

Cited by 39 publications

References 40 publications

Off-shell Amplitudes in Superstring Theory

Off-shell Amplitudes in Superstring Theory

Off‐Shell Amplitudes in String Theory and Hyperbolic Geometry

Introduction

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