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20 Jan 2016 Wronskians, dualities and FZZT- Cardy branes

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Research undertaken during JSPS Summer Programme award now available to view in preprint form. Link: http://arxiv.org/abs/1601.04934

Abstract: The resolvent operator plays a central role in matrix models. For instance, with utilizing the loop equation, all of the perturbative amplitudes including correlators, the free-energy and those of instanton corrections can be obtained from the spectral curve of the resolvent operator. However, at the level of non-perturbative completion, the resolvent operator is generally not sufficient to recover all the information from the loop equations. Therefore it is necessary to find a sufficient set of operators which provide the missing non-perturbative information. In this paper, we study generalized Wronskians of the Baker-Akhiezer systems as a manifestation of these new degrees of freedom. In particular, we derive their isomonodromy systems and then extend several spectral dualities to these systems. In addition, we discuss how these Wronskian operators are naturally aligned on the Kac table. Since they are consistent with the Seiberg-Shih relation, we propose that these new degrees of freedom can be identified as FZZT-Cardy branes in Liouville theory. This means that FZZT-Cardy branes are the bound states of elemental FZZT branes (i.e. the twisted fermions) rather than the bound states of principal FZZT-brane (i.e. the resolvent operator).

Authors: Chuan-Tsung Chan, Hirotaka Irie, Benjamin Niedner, Chi-Hsien Yeh

Posted by Mr. Benjamin Niedner, University of Oxford

04 Jan 2016 Recent papers posted by Professor Andrew Quantock, Cardiff University

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Yamada K, Young RD, Lewis PN, Shinomiya K, Meek KM, Kinoshita S, Caterson B, Quantock AJ. Mesenchymal-epithelial cell interactions and proteoglycan matrix composition in the presumptive stem cell niche of the rabbit corneal limbus. Mol Vis 2015; in press.

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Okumura N, Minamiyama R, Ho LTY, Kay EP, Kawasaki S, Tourtas T, Schlötzer-Schrehardt U, Kruse FE, Young RD, Quantock AJ, Kinoshita S, Koizumi N. Involvement of ZEB1 and Snail1 in excessive production of extracellular matrix in Fuchs endothelial corneal dystrophy. Lab Invest 2015;95:1291-1304.

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Ho LT, Harris AM, Tanioka H, Yagi N, Kinoshita S, Caterson B, Quantock AJ, Young RD, Meek KM. A comparison of glycosaminoglycan distributions, keratan sulphate sulphation patterns and collagen fibril architecture from central to peripheral regions of the bovine cornea. Matrix Biol 2014;38:59-68.

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Koudouna E, Young RD, Ueno M, Kinoshita S, Quantock AJ, Knupp C. Three-dimensional architecture of collagen type VI in the human trabecular meshwork. Mol Vis 2014;20:638-648.

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Hatanaka H, Koizumi N, Okumura N, Takahashi H, Tanioka H, Young RD, Jones FE, Quantock AJ, Kinoshita S. A study of host corneal endothelial cells after non-Descemet stripping automated endothelial keratoplasty. Cornea 2013;32:76-80

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Tanaka Y, Kubota A, Yokokura S, Uematsu M, Shi D, Yamato M, Okano T, Quantock AJ, Nishida K. Optical mechanical refinement of human amniotic membrane by dehydration and cross-linking. J Tissue Engin Regen Med 2012;6:731-737.

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Yamamoto M, Quantock AJ, Young RD, Okumura N, Ueno M, Sakamoto Y, Kinoshita S, Koizumi N. A selective inhibitor of the Rho kinase pathway, Y-27632, and its influence on wound healing in the corneal stroma. Mol Vis 2012;18:1727-1739.