arXiv subjects

Yuji Sugawara

Publications and source records attributed to Yuji Sugawara.

At least 19 recordsLinked to original sources

arXiv2022

Interactions of strings on a T-fold

We consider the interactions of strings on T-folds from the world-sheet point of view which are exact in $α'$. As a concrete example, we take a model where the internal torus at the so(8) enhancement point is twisted by T-duality (T-folded), and compute the scattering amplitudes of a class of massless strings. The four-point amplitudes involving both twisted and untwisted strings are obtained in a closed form in terms of the hypergeometric function. By their factorization, the three-point coupling of the twisted and untwisted strings is found to be suppressed by the chiral momenta along the internal torus, and quantized in integer powers of 1/4. The asymptotic forms of the four-point amplitudes in high-energy limits are also obtained. Our results rely only on general properties of the asymmetric orbifold by the T-duality twist and of the Lie algebra lattice from the symmetry enhancement, and thus may be extended qualitatively to more general T-folds.

hep-th↗

arXiv2022

Notes on Vanishing Cosmological Constant without Bose-Fermi Cancellation

In this article we discuss how one can systematically construct the point particle theories that realize the vanishing one-loop cosmological constant without the bose-fermi cancellation. Our construction is based on the asymmetric (or non-geometric) orbifolds of supersymmetric string vacua. Using the building blocks of their partition functions and their modular properties, we construct the theories which would be naturally identified with certain point particle theories including infinite mass spectra, but not with string vacua. They are obviously non-supersymmetric due to the mismatch of the bosonic and fermionic degrees of freedom at each mass level. Nevertheless, it is found that the one-loop cosmological constant vanishes, after removing the parameter effectively playing the role of the UV cut-off. As concrete examples we demonstrate the constructions of the models based on the toroidal asymmetric orbifolds with the Lie algebra lattices (Englert-Neveu lattices) by making use of the analysis given in [26].

hep-th↗

arXiv2021

Non-SUSY Heterotic String Vacua of Gepner Models with Vanishing Cosmological Constant

We study a natural generalization of that given in [arXiv:2005.13198 [hep-th]] to heterotic string. Namely, starting from the generic Gepner models for Calabi-Yau 3-folds, we construct the non-SUSY heterotic string vacua with the vanishing cosmological constant at the one loop. We especially focus on the asymmetric orbifolding based on some discrete subgroup of the chiral $U(1)$-action which acts on both of the Gepner model and the $SO(32)$ or $E_8\times E_8$-sector. We present a classification of the relevant orbifold models leading to the string vacua with the properties mentioned above. In some cases, the desired vacua can be constructed in the manner quite similar to those given in [arXiv:2005.13198 [hep-th]] for the type II string, in which the orbifold groups contain two generators with the discrete torsions. On the other hand, we also have simpler models that are just realized as the asymmetric orbifolds of cyclic groups with only one generator.

hep-th↗

arXiv2020

Argyres-Douglas Theories, S-duality and AGT Correspondence

We propose a Nekrasov-type formula for the instanton partition functions of four-dimensional N=2 U(2) gauge theories coupled to (A_1,D_{2n}) Argyres-Douglas theories. This is carried out by extending the generalized AGT correspondence to the case of U(2) gauge group, which requires us to define irregular states of the direct sum of Virasoro and Heisenberg algebras. Using our formula, one can evaluate the contribution of the (A_1,D_{2n}) theory at each fixed point on the U(2) instanton moduli space. As an application, we evaluate the instanton partition function of the (A_3,A_3) theory to find it in a peculiar relation to that of SU(2) gauge theory with four fundamental flavors. From this relation, we read off how the S-duality group acts on the UV gauge coupling of the (A_3,A_3) theory.

hep-th↗

arXiv2020

Non-SUSY Gepner Models with Vanishing Cosmological Constant

In this article we discuss a construction of non-SUSY type II string vacua with the vanishing cosmological constant at the one loop level based on the generic Gepner models for Calabi-Yau 3-folds. We make an orbifolding of the Gepner models by $Z_2 \times Z_4$, which asymmetrically acts with some discrete torsions incorporated. We demonstrate that the obtained type II string vacua indeed lead to the vanishing cosmological constant at the one loop, whereas any space-time supercharges cannot be constructed as long as assuming the chiral forms such as '$Q^α_L \equiv \oint dz J_L^α(z)$'. We further discuss possible generalizations of the models described above.

hep-th↗

arXiv2020

Non-Compact SCFT and Mock Modular Forms

One of interesting issues in two-dimensional superconformal field theories is the existence of anomalous modular transformation properties appearing in some non-compact superconformal models, corresponding to the `mock modularity' in mathematical literature. I review a series of my studies on this issue in collaboration with T. Eguchi, mainly focusing on the papers [arXiv:1012.5721 [hep-th]], [arXiv:1407.7721 [hep-th]], [arXiv:1603.02903 [hep-th]].

hep-th↗

arXiv2018

Non-BPS Fractional Branes with Bose-Fermi Cancellation in Asymmetric Orbifolds

We study non-BPS D-branes in the type II string vacua with chiral space-time SUSY constructed based on the asymmetric orbifolds of $\mbox{K3} \cong T^4/{\Bbb Z}_2$ as a succeeding work of arXiv:1704.05262[hep-th]. We especially focus on the fractional D-branes that contains the contributions from the twisted sector of the ${\Bbb Z}_2$ orbifolding. We show that the cylinder partition functions for these fractional branes do not vanish, as in the cases of ordinary non-BPS D-branes. This aspect is in a sharp contrast with the bulk-type branes studied in arXiv:1704.05262[hep-th]. We then discuss the extensions of models by including the discrete torsion depending on the spin structures, and investigate whether we obtain the vanishing self-overlaps associated to the fractional branes. The existence/absence of bose-fermi cancellations both in the closed and open string spectra as well as the massless spectra in the twisted sectors crucially depend on the discrete torsion. We find that some choices of the torsion indeed realize the vanishing self-overlaps for the fractional branes, with keeping the vanishing torus partition function intact.

hep-th↗

arXiv2018

Duality in N=4 Liouville Theory and Moonshine Phenomena

We consider the ${\cal N}=4$ Liouville theory by varying the linear dilaton coupling constant $\cal{Q}$. It is known that at two different values of coupling constant ${\cal Q}=\sqrt{2\over N},-(N-1)\sqrt{2\over N}$ system exhibits two different small ${\cal N}=4$ superconformal symmetries with central charge $c=6$ and $c=6(N-1)$, respectively. In the context of string theory these two theories are considered to describe Coulumb and Higgs branch of the theory and expected to be dual to each other. We study the Mathieu and umbral moonshine phenomena in these two theories and discuss their dual description. We mainly consider the case of $A_N$ type modular invariants.

hep-th↗

arXiv2017

Non-supersymmetric D-branes with Vanishing Cylinder Amplitudes in Asymmetric Orbifolds

We study the type II string vacua with chiral space-time SUSY constructed as asymmetric orbifolds of torus and $ K3 $ compactifications. Despite the fact that all the D-branes are non-BPS in any chiral SUSY vacua, we show that the relevant non-geometric vacua of asymmetric orbifolds allow rather generally configurations of D-branes which lead to vanishing cylinder amplitudes, implying the bose-fermi cancellation at each mass level of the open string spectrum. After working on simple models of toroidal asymmetric orbifolds, we focus on the asymmetric orbifolds of $ T^2 \times {\cal M} $, where $ {\cal M} $ is described by a general $ {\cal N} =4 $ SCFT with $ c=6 $ defined by the Gepner construction for $ K3 $. Even when the modular invariant partition functions in the bulk remain unchanged, the spectra of such non-BPS D-branes with the bose-fermi cancellation can vary significantly according to the choice of orbifolding.

hep-th↗

arXiv2016

Lie algebra lattices and strings on T-folds

We study the world-sheet conformal field theories for T-folds systematically based on the Lie algebra lattices representing the momenta of strings. The fixed point condition required for the T-duality twist restricts the possible Lie algebras. When the T-duality acts as a simple chiral reflection, one is left with the four cases, $A_1, D_{2r}, E_7, E_8$, among the simple simply-laced algebras. From the corresponding Englert-Neveu lattices, we construct the modular invariant partition functions for the T-fold CFTs in bosonic string theory. Similar construction is possible also by using Euclidean even self-dual lattices. We then apply our formulation to the T-folds in the $E_8 \times E_8$ heterotic string theory. Incorporating non-trivial phases for the T-duality twist, we obtain, as simple examples, a class of modular invariant partition functions parametrized by three integers. Our construction includes the cases which are not reduced to the free fermion construction.

hep-th↗

arXiv2016

More on Non-supersymmetric Asymmetric Orbifolds with Vanishing Cosmological Constant

We explore various non-supersymmetric type II string vacua constructed based on asymmetric orbifolds of tori with vanishing cosmological constant at the one loop. The string vacua we present are modifications of the models studied in arXiv:1512.05155[hep-th], of which orbifold group is just generated by a single element. We especially focus on two types of modifications: (i) the orbifold twists include different types of chiral reflections not necessarily removing massless Rarita-Schwinger fields in the 4-dimensional space-time, (ii) the orbifold twists do not include the shift operator. We further discuss the unitarity and stability of constructed non-supersymmetric string vacua, with emphasizing the common features of them.

hep-th↗

arXiv2016

Non-supersymmetric Asymmetric Orbifolds with Vanishing Cosmological Constant

We study type II string vacua defined by torus compactifications accompanied by T-duality twists. We realize the string vacua, specifically, by means of the asymmetric orbifolding associated to the chiral reflections combined with a shift, which are interpreted as describing the compactification on `T-folds'. We discuss possible consistent actions of the chiral reflection on the Ramond-sector of the world-sheet fermions, and explicitly construct non-supersymmetric as well as supersymmetric vacua. Above all, we demonstrate a simple realization of non-supersymmetric vacua with vanishing cosmological constant at one loop. Our orbifold group is generated only by a single element, which results in simpler models than those with such property known previously.

hep-th↗

arXiv2015

Non-geometric Backgrounds Based on Topological Interfaces

We study simple models of the world-sheet CFTs describing non-geometric backgrounds based on the topological interfaces, the `gluing condition' of which imposes T-duality- or analogous twists. To be more specific, we start with the torus partition function on a target space S^1 [base] x (S^1 x S^1) [fiber] with rather general values of radii. The fiber CFT is defined by inserting the twist operators consisting of the topological interfaces which lie along the cycles of the world-sheet torus according to the winding numbers of the base circle. We construct the partition functions involving such duality twists. The modular invariance is achieved straightforwardly, whereas `unitarization' is generically necessary to maintain the unitarity. We demonstrate it in the case of the equal fiber radii. The resultant models are closely related to the CFTs with the discrete torsion. The unitarization is also physically interpreted as multiple insertions of the twist/interface operators along various directions.

hep-th↗

arXiv2014

Compact Formulas for the Completed Mock Modular Forms

In this paper we present a new compact expression of the elliptic genus of SL(2)/U(1)-supercoset theory by making use of the `spectral flow method' of the path-integral evaluation. This new expression is written in a form like a Poincare series with a non-holomorphic Gaussian damping factor, and manifestly shows the modular and spectral flow properties of a real analytic Jacobi form. As a related problem, we present similar compact formulas for the modular completions of various mock modular forms which appear in the representation theory of N=2,4 superconformal algebras. We further discuss the generalization to the cases of arbitrary spin-structures, that is, the world-sheet fermions with twisted boundary conditions parameterized by a continuous parameter. This parameter is naturally identified with the `u-variable' in the Appell-Lerch sum.

hep-th↗

arXiv2014

Comments on Non-holomorphic Modular Forms and Non-compact Superconformal Field Theories

We extend our previous work arXiv:1012.5721 [hep-th] on the non-compact N=2 SCFT_2 defined as the supersymmetric SL(2,R)/U(1)-gauged WZW model. Starting from path-integral calculations of torus partition functions of both the axial-type (`cigar') and the vector-type (`trumpet') models, we study general models of the Z_M-orbifolds and M-fold covers with an arbitrary integer M. We then extract contributions of the degenerate representations (`discrete characters') in such a way that good modular properties are preserved. The `modular completion' of the extended discrete characters introduced in arXiv:1012.5721 [hep-th] are found to play a central role as suitable building blocks in every model of orbifolds or covering spaces. We further examine a large M-limit (the `continuum limit'), which `deconstructs' the spectral flow orbits while keeping a suitable modular behavior. The discrete part of partition function as well as the elliptic genus is then expanded by the modular completions of irreducible discrete characters, which are parameterized by both continuous and discrete quantum numbers modular transformed in a mixed way. This limit is naturally identified with the universal cover of trumpet model. We finally discuss a classification of general modular invariants based on the modular completions of irreducible characters constructed above.

hep-th↗

arXiv2013

`Analytic Continuation' of N=2 Minimal Model

In this paper we discuss what theory should be identified as the `analytic continuation' with $N \rightarrow -N$ of the ${\cal N}=2$ minimal model with the central charge $\hat{c} = 1 - \frac{2}{N}$. We clarify how the elliptic genus of the expected model is written in terms of {\em holomorphic\/} linear combinations of the `modular completions' introduced in [arXiv:1012.5721 [hep-th]] in the $SL(2)_{N+2}/U(1)$-supercoset theory. We further discuss how this model could be interpreted as a kind of {\em `compactified'} model of the $SL(2)_{N+2}/U(1)$-supercoset in the $(\tilde{R},\tilde{R})$-sector, in which only the discrete spectrum appears in the torus partition function and the potential IR-divergence due to the non-compactness of target space is removed. We also briefly argue on possible definitions of the sectors with other spin structures.

hep-th↗

arXiv2012

Thermodynamics of Superstring on Near-extremal NS5 and Effective Hagedorn Behavior

We study the thermodynamical torus partition function of superstring on the near-extremal black NS5-brane background. The exact partition function has been computed with the helps of our previous works:[arXiv:1012.5721 [hep-th]], [arXiv:1109.3365 [hep-th]], and naturally decomposed into two parts. The first part is contributed from strings freely propagating in the asymptotic region, which are identified as the superstring gas at the Hawking temperature on the linear-dilaton background. The second part includes the contribution localized around the `tip of cigar', which characterizes the non-extremality. Remarkably, the latter part includes massless excitations with non-vanishing thermal winding, which signifies that the Hagedorn-like behavior effectively appears, even though the Hawking temperature is much lower than the Hagedorn temperature. We also explore the high-temperature backgrounds defined by the orbifolding along the Euclidean time direction. In those cases, the thermal winding modes localized around the tip are found to be tachyonic, reflecting the singularities of Euclidean backgrounds caused by orbifolding.

hep-th↗

arXiv2011

Non-holomorphic Modular Forms and SL(2,R)/U(1) Superconformal Field Theory

We study the torus partition function of the SL(2,R)/U(1) SUSY gauged WZW model coupled to N=2 U(1) current. Starting from the path-integral formulation of the theory, we introduce an infra-red regularization which preserves good modular properties and discuss the decomposition of the partition function in terms of the N=2 characters of discrete (BPS) and continuous (non-BPS) representations. Contrary to our naive expectation, we find a non-holomorphic dependence (dependence on \barτ) in the expansion coefficients of continuous representations. This non-holomorphicity appears in such a way that the anomalous modular behaviors of the discrete (BPS) characters are compensated by the transformation law of the non-holomorphic coefficients of the continuous (non-BPS) characters. Discrete characters together with the non-holomorphic continuous characters combine into real analytic Jacobi forms and these combinations exactly agree with the "modular completion" of discrete characters known in the theory of Mock theta functions \cite{Zwegers}. We consider this to be a general phenomenon: we expect to encounter "holomorphic anomaly" (\barτ-dependence) in string partition function on non-compact target manifolds. The anomaly occurs due to the incompatibility of holomorphy and modular invariance of the theory. Appearance of non-holomorphicity in SL(2,R)/U(1) elliptic genus has recently been observed by Troost \cite{Troost}.

hep-th↗