arXiv subjects

Thomas Creutzig

Publications and source records attributed to Thomas Creutzig.

At least 127 records · Page 7Linked to original sources

arXiv2013

A commutant realization of Odake's algebra

The bcβγ-system W of rank 3 has an action of the affine vertex algebra V_0(sl_2), and the commutant vertex algebra C =Com(V_0(sl_2), W) contains copies of V_{-3/2}(sl_2) and Odake's algebra O. Odake's algebra is an extension of the N=2 superconformal algebra with c=9, and is generated by eight fields which close nonlinearly under operator product expansions. Our main result is that V_{-3/2}(sl_2) and O form a Howe pair (i.e., a pair of mutual commutants) inside C. More generally, any finite-dimensional representation of a Lie algebra g gives rise to a similar Howe pair, and this example corresponds to the adjoint representation of sl_2.

math.QA↗

arXiv2013

The super W_{1+\infty} algebra with integral central charge

The Lie superalgebra SD of regular differential operators on the super circle has a universal central extension \hat{SD}. For each c\in C, the vacuum module M_c(\hat{SD}) of central charge c admits a vertex superalgebra structure, and M_c(\hat{SD}) \cong M_{-c}(\hat{SD}). The irreducible quotient V_c(\hat{SD}) of the vacuum module is known as the super W_{1+\infty} algebra. We show that for each integer n>0, V_n(\hat{SD}) has a minimal strong generating set consisting of 4n fields, and we identify it with a W-algebra associated to the purely odd simple root system of gl(n|n). Finally, we realize V_n(\hat{SD}) as the limit of a family of commutant vertex algebras that generically have the same graded character and possess a minimal strong generating set of the same cardinality.

math.QA↗

arXiv2013

N=1 supersymmetric higher spin holography on AdS_3

We propose a duality between a higher spin N=1 supergravity on AdS_3 and a large N limit of a family of N=(1,1) superconformal field theories. The gravity theory is an N=1 truncation of the N=2 supergravity found by Prokushkin and Vasiliev, and the dual conformal field theory is defined by a supersymmetric coset model. We check this conjecture by comparing one loop partition functions and find agreement. Moreover, we study the symmetry of the dual coset model and in particular compute fields of the coset algebra of dimension 3/2, 2, 2 and 5/2 explicitely.

hep-th↗

arXiv2013

Relating the Archetypes of Logarithmic Conformal Field Theory

Logarithmic conformal field theory is a rich and vibrant area of modern mathematical physics with well-known applications to both condensed matter theory and string theory. Our limited understanding of these theories is based upon detailed studies of various examples that one may regard as archetypal. These include the c=-2 triplet model, the Wess-Zumino-Witten model on SL(2;R) at level k=-1/2, and its supergroup analogue on GL(1|1). Here, the latter model is studied algebraically through representation theory, fusion and modular invariance, facilitating a subsequent investigation of its cosets and extended algebras. The results show that the archetypes of logarithmic conformal field theory are in fact all very closely related, as are many other examples including, in particular, the SL(2|1) models at levels 1 and -1/2. The conclusion is then that the archetypal examples of logarithmic conformal field theory are practically all the same, so we should not expect that their features are in any way generic. Further archetypal examples must be sought.

hep-th↗

arXiv2012

Three point functions in higher spin AdS_3 supergravity

In a previous work we have proposed that the Prokushkin-Vasiliev higher spin N=2 supergravity on AdS_3 is dual to a large N limit of the N=(2,2) CP^N Kazama-Suzuki model. There is now strong evidence supporting this proposal based on symmetry and spectrum comparison. In this paper we will give further evidence for the duality by studying correlation functions. We compute boundary three point functions with two fermionic operators and one higher spin bosonic current in terms of the bulk supergravity theory. Then we compare with the results in the dual CFT, where the supersymmetry of the theory turns out to be very helpful. In particular we use it to confirm results conjectured in the bosonic case. Moreover, correlators with a fermionic current can be obtained via supersymmetry.

hep-th↗

arXiv2012

A commutant realization of W^(2)_n at critical level

For n\geq 2, there is a free field realization of the affine vertex superalgebra A associated to psl(n|n) at critical level inside the bcβγsystem W of rank n^2. We show that the commutant C=Com(A,W) is purely bosonic and is freely generated by n+1 fields. We identify the Zhu algebra of C with the ring of invariant differential operators on the space of n\times n matrices under SL_n \times SL_n, and we classify the irreducible, admissible C-modules with finite dimensional graded pieces. For n\leq 4, C is isomorphic to the W_n^{(2)}-algebra at critical level, and we conjecture that this holds for all n.

math.QA↗

arXiv2012

Modular Data and Verlinde Formulae for Fractional Level WZW Models I

The modular properties of fractional level affine sl(2)-theories and, in particular, the application of the Verlinde formula, have a long and checkered history in conformal field theory. Recent advances in logarithmic conformal field theory have led to the realisation that problems with fractional level models stem from trying to build the theory with an insufficiently rich category of representations. In particular, the appearance of negative fusion coefficients for admissible highest weight representations is now completely understood. Here, the modular story for certain fractional level theories is completed. Modular transformations are derived for the complete set of admissible irreducible representations when the level is k=-1/2 or k=-4/3. The S-matrix data and Verlinde formula are then checked against the known fusion rules with complete agreement. Finally, an infinite set of modular invariant partition functions is constructed in each case.

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arXiv2012

The Mock Modular Data of a Family of Superalgebras

The modular properties of characters of representations of a family of W-superalgebras extending the affine Lie superalgebra of gl(1|1) are considered. Modules fall into two classes, the generic type and the non-generic one. Characters of non-generic modules are expressed in terms of higher-level Appell-Lerch sums. We compute the modular transformations of characters and interpret the Mordell integral as an integral over characters of generic representations. The \C-span of a finite number of non-generic characters together with an uncountable set of characters of the generic type combine into a representation of SL(2;\Z). The modular transformations are then used to define a product on the space of characters. The fusion rules of the extended algebras are partially inherited from the known fusion rules for modules of the affine Lie superalgebra of gl(1|1). Moreover, the product obtained from the modular transformations coincides with the product of the Grothendieck ring of characters if and only if the fusion multiplicities are at most one.

math.NT↗

arXiv2011

Fermionic Coset, Critical Level W^(2)_4-Algebra and Higher Spins

The fermionic coset is a limit of the pure spinor formulation of the AdS5xS5 sigma model as well as a limit of a nonlinear topological A-model, introduced by Berkovits. We study the latter, especially its symmetries, and map them to higher spin algebras. We show the following. The linear A-model possesses affine $\AKMSA{pgl}{4}{4}_0$ symmetry at critical level and its $\AKMSA{psl}{4}{4}_0$ current-current perturbation is the nonlinear model. We find that the perturbation preserves $\mathcal{W}^{(2)}_4$-algebra symmetry at critical level. There is a topological algebra associated to $\AKMSA{pgl}{4}{4}_0$ with the properties that the perturbation is BRST-exact. Further, the BRST-cohomology contains world-sheet supersymmetric symplectic fermions and the non-trivial generators of the $\mathcal{W}^{(2)}_4$-algebra. The Zhu functor maps the linear model to a higher spin theory. We analyze its $\SLSA{psl}{4}{4}$ action and find finite dimensional short multiplets.

hep-th↗

arXiv2011

W-Algebras Extending Affine gl(1|1)

It was recently shown that gl^(1|1) admits an infinite family of simple current extensions. Here, these findings are reviewed and explicit free field realisations of the extended algebras are constructed. The leading contributions to the operator product algebra are then calculated. Among these extensions, one finds four infinite families that seem to contain, as subalgebras, copies of the W^(2)_N algebras of Feigin and Semikhatov at various levels and central charges +/- 1.

hep-th↗

arXiv2011

Higher spin AdS_3 supergravity and its dual CFT

Vasiliev's higher spin supergravity theory on three dimensional anti-de Sitter space is studied and, in particular, the partition function is computed at one loop level. The dual conformal field theory is proposed to be the N=(2,2) CP^N Kazama-Suzuki model in two dimensions. The proposal is based on symmetry considerations and comparison of the bulk partition function with the conformal field theory. Our findings suggest that the theory is strong-weak self-dual.

hep-th↗

arXiv2011

The FZZ duality with boundary

The Fateev-Zamolodchikov-Zamolodchikov (FZZ) duality relates Witten's cigar model to sine-Liouville theory. This duality was proven in the path integral formulation and extended to the case of higher genus closed Riemann surfaces by Schomerus and one of the authors. In this note we further extend the duality to the case with boundary. Specifically, we relate D1-branes in the cigar model to D2-branes in the sine-Liouville theory. In particular, the boundary action for D2-branes in the sine-Liouville theory is constructed. We also consider the fermionic version of the FZZ duality. This duality was proven as a mirror symmetry by Hori and Kapustin, but we give an alternative proof in the path integral formulation which directly relates correlation functions. Also here the case with boundary is investigated and the results are consistent with those for branes in N=2 super Liouville field theory obtained by Hosomichi.

hep-th↗

arXiv2011

Supergroup - extended super Liouville correspondence

We derive a relation between correlation functions of supergroup WZNW models and conformal field theories with extended superconformal symmetry. The supergroups considered have a bosonic subgroup of the form SL(2) x A for some Lie group A. The corresponding conformal field theory is a super Liouville field theory coupled with the WZNW model on A. An example is a correspondence between the PSU(1,1|2) WZNW model and small N=4 super Liouville field theory. The OSP(n|2) WZNW model is related to a superconformal field theory with SO(n) extended superconformal symmetry of the Knizhnik-Bershadsky type. In the case n=4 this is simply the large N=(4,4) superconformal symmetry. Besides these two examples we make a general derivation encompassing the WZNW models on supergroups SL(2|n), D(2,1;α), OSP(4|2n), F(4) and G(3) and their relation to models with extended superconformal algebras as symmetry.

hep-th↗

arXiv2010

Yangian Superalgebras in Conformal Field Theory

Quantum Yangian symmetry in several sigma models with supergroup or supercoset as target is established. Starting with a two-dimensional conformal field theory that has current symmetry of a Lie superalgebra with vanishing Killing form we construct non-local charges and compute their properties. Yangian axioms are satisfied, except that the Serre relations only hold for a subsector of the space of fields. Yangian symmetry implies that correlation functions of fields in this sector satisfy Ward identities. We then show that this symmetry is preserved by certain perturbations of the conformal field theory. The main example are sigma models of the supergroups PSL(N|N), OSP(2N+2|2N) and D(2,1;α) away from the WZW point. Further there are the OSP(2N+2|2N) Gross-Neveu models and current-current perturbations of ghost systems, both for the disc as world-sheet. The latter we show to be equivalent to CP^{N-1|N} sigma models, while the former are conjecturally dual to supersphere sigma models.

hep-th↗

arXiv2010

Yangian in the Twistor String

We study symmetries of the quantized open twistor string. In addition to global PSL(4|4) symmetry, we find non-local conserved currents. The associated non-local charges lead to Ward identities which show that these charges annihilate the string gluon tree amplitudes, and have the same form as symmetries of amplitudes in N=4 super conformal Yang Mills theory. We describe how states of the open twistor string form a realization of the PSL(4|4) Yangian superalgebra.

hep-th↗

arXiv2010

From world-sheet supersymmetry to super target spaces

We investigate the relation between N=(2,2) superconformal Lie group WZNW models and Lie supergroup WZNW models. The B-twist of an exactly marginal perturbation of the world-sheet superconformal sigma model is the supergroup model. Moreover, the superconformal currents are expressed in terms of Lie superalgebra currents in the twisted theory. As applications, we find protected sectors and boundary actions in the supergroup sigma model. A special example is the relation between string theory on AdS_3 x S^3 x T^4 in the RNS formalism and the U(1,1|2) x U(1|1) x U(1|1) supergroup WZNW model.

hep-th↗

arXiv2010

Branes in the OSP(1|2) WZNW model

The boundary OSP(1|2) WZNW model possesses two types of branes, which are localized on supersymmetric Euclidean AdS$_2$ and on two-dimensional superspheres. We compute the coupling of closed strings to these branes with two different methods. The first one uses factorization constraints and the other one a correspondence to boundary N=1 super-Liouville field theory, which we proof with path integral techniques. We check that the results obey the Cardy condition and reproduce the semi-classical computations. For the check we also compute the spectral density of open strings that are attached to the non-compact branes.

hep-th↗

arXiv2010

N=2 Superconformal Symmetry in Super Coset Models

We extend the Kazama-Suzuki construction of models with N=(2,2) world-sheet supersymmetry to cosets S/K of supergroups. Among the admissible target spaces that allow for an extension to N=2 superconformal algebras are some simple Lie supergroups, including PSL(N|N). Our general analysis is illustrated at the example of the N=1 WZNW model on GL(1|1). After constructing its N=2 superconformal algebra we determine the (anti-)chiral ring of the theory. It exhibits an interesting interplay between world-sheet and target space supersymmetry.

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