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Renormalization of Twisted Ramond Fields in D1-D5 SCFT$_2$
High Energy Physics - Theory · Submitted 1 Oct 2020
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The second order correction (in the deformation parameter) to the two-point function of the Ramond fields, defined as double integrals over this four-point function, turns out to be UV-divergent, requiring an appropriate renormalization of the fields.
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The abstract, sentence by sentence
We explore the Ramond sector of the deformed two-dimensional $\cal N = (4, 4)$ superconformal $(T^4)^N /S_N$ orbifold theory, describing bound states of D1-D5 brane system in type IIB superstring. We derive the large-$N$ limit of the four-point function of two R-charged twisted Ramond fields and two marginal deformation operators at the free orbifold point. Specific short-distance limits of this function provide several structure constants, the OPE fusion rules and the conformal dimensions of a few non-BPS operators. The second order correction (in the deformation parameter) to the two-point function of the Ramond fields, defined as double integrals over this four-point function, turns out to be UV-divergent, requiring an appropriate renormalization of the fields. We calculate the corrections to the conformal dimensions of the twisted Ramond ground states at the large-$N$ limit. The same integral yields the first-order deviation from zero of the structure constant of the three-point function of two Ramond fields and one deformation operator. Similar results concerning the correction to the two-point function of bare twist operators and their renormalization are also obtained.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We explore the Ramond sector of the deformed two-dimensional $\cal N = (4, 4)$ superconformal $(T^4)^N /S_N$ orbifold theory, describing bound states of D1-D5 brane system in type IIB superstring. | contribution 0.54 | 0.77 | 0.04 | asserted 0.94 |
| s1 | We derive the large-$N$ limit of the four-point function of two R-charged twisted Ramond fields and two marginal deformation operators at the free orbifold point. | contribution 0.50 | 0.96 | 0.10 | asserted 1.00 |
| s2 | Specific short-distance limits of this function provide several structure constants, the OPE fusion rules and the conformal dimensions of a few non-BPS operators. | result 0.92 | 0.91 | 0.14 | asserted 1.00 |
| s3 | The second order correction (in the deformation parameter) to the two-point function of the Ramond fields, defined as double integrals over this four-point function, turns out to be UV-divergent, requiring an appropriate renormalization of the fields. | result 0.95 | 0.94 | 0.31 | asserted 1.00 |
| s4 | We calculate the corrections to the conformal dimensions of the twisted Ramond ground states at the large-$N$ limit. | result 0.66 | 0.96 | 0.22 | asserted 1.00 |
| s5 | The same integral yields the first-order deviation from zero of the structure constant of the three-point function of two Ramond fields and one deformation operator. | result 1.00 | 0.93 | 0.11 | asserted 1.00 |
| s6 | Similar results concerning the correction to the two-point function of bare twist operators and their renormalization are also obtained. | result 0.93 | 0.90 | 0.06 | asserted 1.00 |
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The paper
Original abstract
We explore the Ramond sector of the deformed two-dimensional $\cal N = (4, 4)$ superconformal $(T^4)^N /S_N$ orbifold theory, describing bound states of D1-D5 brane system in type IIB superstring. We derive the large-$N$ limit of the four-point function of two R-charged twisted Ramond fields and two marginal deformation operators at the free orbifold point. Specific short-distance limits of this function provide several structure constants, the OPE fusion rules and the conformal dimensions of a few non-BPS operators. The second order correction (in the deformation parameter) to the two-point function of the Ramond fields, defined as double integrals over this four-point function, turns out to be UV-divergent, requiring an appropriate renormalization of the fields. We calculate the corrections to the conformal dimensions of the twisted Ramond ground states at the large-$N$ limit. The same integral yields the first-order deviation from zero of the structure constant of the three-point function of two Ramond fields and one deformation operator. Similar results concerning the correction to the two-point function of bare twist operators and their renormalization are also obtained.
Human review
How the literature uses it
14 arXiv papers cite this in 65 sentences
Papers citing it · 28 sentences without a confident label
Builds on it 1 paper
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The purpose of the present paper is to discuss the effect of $$ on the R-neutral Ramond ground states of the $n$-twisted sector, extending the analysis of R-charged Ramond fields $R^±_n$ done in [ref] , and thus forming a complete picture for all single-cycle Ramond ground states in the deformed CFT ([ref]).
Dynamics of R-neutral Ramond fields in the D1-D5 SCFT · Introduction · 1.00
Uses its method or tool 4 papers
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While the first-order correction vanishes, we show, following the regularization developed in [ref] , that the second-order correction does not, so $R^0±_n$ is lifted at order $^2$, and at the leading order in the large-$N$ expansion.
Dynamics of R-neutral Ramond fields in the D1-D5 SCFT · Introduction · 0.93
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The final result for the base sphere four-point function, parameterized by $x$, is ([ref]), i.e. $x = e^S_L x_$, where $e^S_L$ is the bare-twist correlation function; using either the results in [ref] or the stress-tensor method of [ref] , we can find [equation] apart from a constant which we fix later by looking at OPE limits of the final correlator.
Four-point functions with multi-cycle fields in symmetric orbifolds and the D1-D5 CFT · Derivation of the master formula · 0.89
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One can use the stress-tensor method allied with the covering surface technique to compute the non-composite functions $G_m_p(u,u̅)$, $p = 1,2$, as well; see [ref] .
Correlation functions of composite Ramond fields in deformed D1-D5 orbifold SCFT$_2$ · Non-composite contributions and the full function. · 0.87
Uses its data or values 2 papers
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The leading coefficients in the expansions ([ref])-([ref]) are the structure constants of the operators involved in the respective OPE channels, which can be expressed in terms of three-point functions: [equation] To obtain ([ref]) we have used the structure constant $⟨_2 _3 _2 ⟩= 2^13/3 3^4$, derived in [ref] .
Dynamics of R-neutral Ramond fields in the D1-D5 SCFT · OPE channels · 1.00
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The structure constant $⟨_(2) _(3) _(2) ⟩$ has been computed in [ref] [See Eq.(C.5) ibid.] ⟨_(2) _(3) _(2) ⟩= 2^13/3 3^4 , yielding the structure constants $⟨R^ζ_1_(n_1) R^ζ_2_(n_2) ^†_(3) R^ζ_1_(n_1) R^ζ_2_(n_2) ⟩$, listed in App.[ref], Eq.([ref]).
On the Dynamics of Protected Ramond Ground States in the D1-D5 CFT · Different twists $n_1 ≠n_2$ · 1.00
Compares with it 3 papers
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When applied to the bare twist fields correlation function, the stress-tensor method becomes quite trivial [ref] , and here, when we compute the Liouville factor for the same covering map (with a specific parameterization and for $g = 0$, i.e. in the large-$N$ limit), we can check that both results agree.
Dynamics of R-neutral Ramond fields in the D1-D5 SCFT · Introduction · 0.96
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The behavior in Eqs.([ref]) and ([ref]) matches precisely the one found for the disconnected functions $G_m_p$, described in detail in [ref] .
Correlation functions of composite Ramond fields in deformed D1-D5 orbifold SCFT$_2$ · OPE of two deformation operators. · 0.99
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In the limit $u →1$ we obtain the fusion rule $[] ×[]$, which must agree with the results found elsewhere [ref] in other correlation functions involving two deformation operators.
On the Dynamics of Protected Ramond Ground States in the D1-D5 CFT · Different twists $n_1 ≠n_2$ · 0.98
Cites it as background 9 papers
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See [ref] for details, and also [ref] for interesting expositions on conformal perturbation theory.
On the Dynamics of Protected Ramond Ground States in the D1-D5 CFT · The interacting CFT and renormalization · 0.84
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states, see [ref] .
Partial Spectral Flow in the D1D5 CFT · The Gava-Narain method · 0.94
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Changes to higher $n$-point function data have been discussed more rarely, however, see [ref] for general considerations for deforming structure constants, and for specific cases [ref] .
Conformal Perturbation Theory for $n$-Point Functions: Structure Constant Deformation · Introduction and summary · 0.92
What it cites · 41 sentences without a confident label
Uses the method or tool of 7 papers
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We will present a detailed derivation of the large-$N$ approximation of the corresponding functions, by applying covering surface techniques [ref] combined with the `stress-tensor method' [ref] .
Correlation functions for M^N/S_N orbifolds · Introduction · 1.00
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We will present a detailed derivation of the large-$N$ approximation of the corresponding functions, by applying covering surface techniques [ref] combined with the `stress-tensor method' [ref] .
Three-point functions for M^N/S^N orbifolds with N=4 supersymmetry · Introduction · 1.00
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Our computation of the leading term in the $1/N$ expansion of the connected part of ([ref]), takes into account only the terms contributing to genus zero surfaces, i.e. we use the well known map [ref] between the “base” branched sphere to its genus-zero covering surface [ref] .
Four graviton scattering amplitude from $S^N\large{{\bf R}}^{8}$ supersymmetric orbifold sigma model · Introduction · 0.97
Compares with 3 papers
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The same function has been computed in App.E of Ref. [ref] , but using a different parameterization map $u(x)$, in place of ([ref]) (hence their function $G(x)$ is different from ours).
A Spin Chain for the Symmetric Product CFT_2 · Bare twists · 1.00
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Explicitly [equation] This agrees with the result of Ref. [ref] , again, apart from an overall factor of $1/6$.
Correlation functions for M^N/S_N orbifolds · OPEs with bare twists and structure constants · 1.00
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Our results for the non-BPS fields are consistent with what is known about the chiral NS and twisted sectors [ref] .
Operator mixing in deformed D1D5 CFT and the OPE on the cover · Introduction · 0.89
Cites as background 49 papers
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The standard way [ref] of implementing the boundary conditions ([ref]) for $G(u,u̅)$ is to map the `base sphere' $S^2_base = ℂ ∪∞$ to a ramified `covering surface' $Σ_cover$, whose ramification points correspond to the position and the order of twists operators.
Correlation functions for M^N/S_N orbifolds · The covering surface · 0.90
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The present paper investigates the effects on the conformal properties of twisted ground states in the $N = (4,4)$ orbifold SCFT$_2$ when the theory is deformed by a marginal scalar modulus operator $λ$ [ref] .
Excitations in the deformed D1D5 CFT · Introduction · 0.83
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The present paper investigates the effects on the conformal properties of twisted ground states in the $N = (4,4)$ orbifold SCFT$_2$ when the theory is deformed by a marginal scalar modulus operator $λ$ [ref] .
Full action of two deformation operators in the D1D5 CFT · Introduction · 0.83
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