Partial domain wall partition functions

Abstract We consider six-vertex model configurations on an (n × N) lattice, n ≤ N, that satisfy a variation on domain wall boundary conditions that we define and call partial domain wall boundary conditions. We obtain two expressions for the corresponding partial domain wall partition function, as a...
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Gespeichert in:

Autor*in:	Foda, O. [verfasserIn] Wheeler, M.

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2012

Schlagwörter:	Lattice Integrable Models Integrable Hierarchies

Anmerkung:	© SISSA 2012

Übergeordnetes Werk:	Enthalten in: Journal of high energy physics - Berlin : Springer, 1997, 2012(2012), 7 vom: 30. Juli
Übergeordnetes Werk:	volume:2012 ; year:2012 ; number:7 ; day:30 ; month:07

Links:	Volltext

DOI / URN:	10.1007/JHEP07(2012)186

Katalog-ID:	SPR030424011

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520			\|a Abstract We consider six-vertex model configurations on an (n × N) lattice, n ≤ N, that satisfy a variation on domain wall boundary conditions that we define and call partial domain wall boundary conditions. We obtain two expressions for the corresponding partial domain wall partition function, as an (N × N)-determinant and as an (n × n)-determinant. The latter was first obtained by I Kostov. We show that the two determinants are equal, as expected from the fact that they are partition functions of the same object, that each is a discrete KP τ-function, and, recalling that these determinants represent tree-level structure constants in $ \mathcal{N} = 4\;{\text{SYM}} $, we show that introducing 1-loop corrections, as proposed by N Gromov and P Vieira, preserves the determinant structure.
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Indexfelder

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allfields	10.1007/JHEP07(2012)186 doi (DE-627)SPR030424011 (SPR)JHEP07(2012)186-e DE-627 ger DE-627 rakwb eng Foda, O. verfasserin aut Partial domain wall partition functions 2012 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © SISSA 2012 Abstract We consider six-vertex model configurations on an (n × N) lattice, n ≤ N, that satisfy a variation on domain wall boundary conditions that we define and call partial domain wall boundary conditions. We obtain two expressions for the corresponding partial domain wall partition function, as an (N × N)-determinant and as an (n × n)-determinant. The latter was first obtained by I Kostov. We show that the two determinants are equal, as expected from the fact that they are partition functions of the same object, that each is a discrete KP τ-function, and, recalling that these determinants represent tree-level structure constants in $ \mathcal{N} = 4\;{\text{SYM}} $, we show that introducing 1-loop corrections, as proposed by N Gromov and P Vieira, preserves the determinant structure. Lattice Integrable Models (dpeaa)DE-He213 Integrable Hierarchies (dpeaa)DE-He213 Wheeler, M. aut Enthalten in Journal of high energy physics Berlin : Springer, 1997 2012(2012), 7 vom: 30. Juli (DE-627)320910571 (DE-600)2027350-2 1029-8479 nnns volume:2012 year:2012 number:7 day:30 month:07 https://dx.doi.org/10.1007/JHEP07(2012)186 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_40 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_161 GBV_ILN_293 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2064 GBV_ILN_2068 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4338 AR 2012 2012 7 30 07
spelling	10.1007/JHEP07(2012)186 doi (DE-627)SPR030424011 (SPR)JHEP07(2012)186-e DE-627 ger DE-627 rakwb eng Foda, O. verfasserin aut Partial domain wall partition functions 2012 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © SISSA 2012 Abstract We consider six-vertex model configurations on an (n × N) lattice, n ≤ N, that satisfy a variation on domain wall boundary conditions that we define and call partial domain wall boundary conditions. We obtain two expressions for the corresponding partial domain wall partition function, as an (N × N)-determinant and as an (n × n)-determinant. The latter was first obtained by I Kostov. We show that the two determinants are equal, as expected from the fact that they are partition functions of the same object, that each is a discrete KP τ-function, and, recalling that these determinants represent tree-level structure constants in $ \mathcal{N} = 4\;{\text{SYM}} $, we show that introducing 1-loop corrections, as proposed by N Gromov and P Vieira, preserves the determinant structure. Lattice Integrable Models (dpeaa)DE-He213 Integrable Hierarchies (dpeaa)DE-He213 Wheeler, M. aut Enthalten in Journal of high energy physics Berlin : Springer, 1997 2012(2012), 7 vom: 30. Juli (DE-627)320910571 (DE-600)2027350-2 1029-8479 nnns volume:2012 year:2012 number:7 day:30 month:07 https://dx.doi.org/10.1007/JHEP07(2012)186 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_40 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_161 GBV_ILN_293 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2064 GBV_ILN_2068 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4338 AR 2012 2012 7 30 07
allfields_unstemmed	10.1007/JHEP07(2012)186 doi (DE-627)SPR030424011 (SPR)JHEP07(2012)186-e DE-627 ger DE-627 rakwb eng Foda, O. verfasserin aut Partial domain wall partition functions 2012 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © SISSA 2012 Abstract We consider six-vertex model configurations on an (n × N) lattice, n ≤ N, that satisfy a variation on domain wall boundary conditions that we define and call partial domain wall boundary conditions. We obtain two expressions for the corresponding partial domain wall partition function, as an (N × N)-determinant and as an (n × n)-determinant. The latter was first obtained by I Kostov. We show that the two determinants are equal, as expected from the fact that they are partition functions of the same object, that each is a discrete KP τ-function, and, recalling that these determinants represent tree-level structure constants in $ \mathcal{N} = 4\;{\text{SYM}} $, we show that introducing 1-loop corrections, as proposed by N Gromov and P Vieira, preserves the determinant structure. Lattice Integrable Models (dpeaa)DE-He213 Integrable Hierarchies (dpeaa)DE-He213 Wheeler, M. aut Enthalten in Journal of high energy physics Berlin : Springer, 1997 2012(2012), 7 vom: 30. Juli (DE-627)320910571 (DE-600)2027350-2 1029-8479 nnns volume:2012 year:2012 number:7 day:30 month:07 https://dx.doi.org/10.1007/JHEP07(2012)186 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_40 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_161 GBV_ILN_293 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2064 GBV_ILN_2068 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4338 AR 2012 2012 7 30 07
allfieldsGer	10.1007/JHEP07(2012)186 doi (DE-627)SPR030424011 (SPR)JHEP07(2012)186-e DE-627 ger DE-627 rakwb eng Foda, O. verfasserin aut Partial domain wall partition functions 2012 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © SISSA 2012 Abstract We consider six-vertex model configurations on an (n × N) lattice, n ≤ N, that satisfy a variation on domain wall boundary conditions that we define and call partial domain wall boundary conditions. We obtain two expressions for the corresponding partial domain wall partition function, as an (N × N)-determinant and as an (n × n)-determinant. The latter was first obtained by I Kostov. We show that the two determinants are equal, as expected from the fact that they are partition functions of the same object, that each is a discrete KP τ-function, and, recalling that these determinants represent tree-level structure constants in $ \mathcal{N} = 4\;{\text{SYM}} $, we show that introducing 1-loop corrections, as proposed by N Gromov and P Vieira, preserves the determinant structure. Lattice Integrable Models (dpeaa)DE-He213 Integrable Hierarchies (dpeaa)DE-He213 Wheeler, M. aut Enthalten in Journal of high energy physics Berlin : Springer, 1997 2012(2012), 7 vom: 30. Juli (DE-627)320910571 (DE-600)2027350-2 1029-8479 nnns volume:2012 year:2012 number:7 day:30 month:07 https://dx.doi.org/10.1007/JHEP07(2012)186 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_40 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_161 GBV_ILN_293 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2064 GBV_ILN_2068 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4338 AR 2012 2012 7 30 07
allfieldsSound	10.1007/JHEP07(2012)186 doi (DE-627)SPR030424011 (SPR)JHEP07(2012)186-e DE-627 ger DE-627 rakwb eng Foda, O. verfasserin aut Partial domain wall partition functions 2012 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © SISSA 2012 Abstract We consider six-vertex model configurations on an (n × N) lattice, n ≤ N, that satisfy a variation on domain wall boundary conditions that we define and call partial domain wall boundary conditions. We obtain two expressions for the corresponding partial domain wall partition function, as an (N × N)-determinant and as an (n × n)-determinant. The latter was first obtained by I Kostov. We show that the two determinants are equal, as expected from the fact that they are partition functions of the same object, that each is a discrete KP τ-function, and, recalling that these determinants represent tree-level structure constants in $ \mathcal{N} = 4\;{\text{SYM}} $, we show that introducing 1-loop corrections, as proposed by N Gromov and P Vieira, preserves the determinant structure. Lattice Integrable Models (dpeaa)DE-He213 Integrable Hierarchies (dpeaa)DE-He213 Wheeler, M. aut Enthalten in Journal of high energy physics Berlin : Springer, 1997 2012(2012), 7 vom: 30. Juli (DE-627)320910571 (DE-600)2027350-2 1029-8479 nnns volume:2012 year:2012 number:7 day:30 month:07 https://dx.doi.org/10.1007/JHEP07(2012)186 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_40 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_161 GBV_ILN_293 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2064 GBV_ILN_2068 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4338 AR 2012 2012 7 30 07
language	English
source	Enthalten in Journal of high energy physics 2012(2012), 7 vom: 30. Juli volume:2012 year:2012 number:7 day:30 month:07
sourceStr	Enthalten in Journal of high energy physics 2012(2012), 7 vom: 30. Juli volume:2012 year:2012 number:7 day:30 month:07
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author	Foda, O.
spellingShingle	Foda, O. misc Lattice Integrable Models misc Integrable Hierarchies Partial domain wall partition functions
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topic_title	Partial domain wall partition functions Lattice Integrable Models (dpeaa)DE-He213 Integrable Hierarchies (dpeaa)DE-He213
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title_sort	partial domain wall partition functions
title_auth	Partial domain wall partition functions
abstract	Abstract We consider six-vertex model configurations on an (n × N) lattice, n ≤ N, that satisfy a variation on domain wall boundary conditions that we define and call partial domain wall boundary conditions. We obtain two expressions for the corresponding partial domain wall partition function, as an (N × N)-determinant and as an (n × n)-determinant. The latter was first obtained by I Kostov. We show that the two determinants are equal, as expected from the fact that they are partition functions of the same object, that each is a discrete KP τ-function, and, recalling that these determinants represent tree-level structure constants in $ \mathcal{N} = 4\;{\text{SYM}} $, we show that introducing 1-loop corrections, as proposed by N Gromov and P Vieira, preserves the determinant structure. © SISSA 2012
abstractGer	Abstract We consider six-vertex model configurations on an (n × N) lattice, n ≤ N, that satisfy a variation on domain wall boundary conditions that we define and call partial domain wall boundary conditions. We obtain two expressions for the corresponding partial domain wall partition function, as an (N × N)-determinant and as an (n × n)-determinant. The latter was first obtained by I Kostov. We show that the two determinants are equal, as expected from the fact that they are partition functions of the same object, that each is a discrete KP τ-function, and, recalling that these determinants represent tree-level structure constants in $ \mathcal{N} = 4\;{\text{SYM}} $, we show that introducing 1-loop corrections, as proposed by N Gromov and P Vieira, preserves the determinant structure. © SISSA 2012
abstract_unstemmed	Abstract We consider six-vertex model configurations on an (n × N) lattice, n ≤ N, that satisfy a variation on domain wall boundary conditions that we define and call partial domain wall boundary conditions. We obtain two expressions for the corresponding partial domain wall partition function, as an (N × N)-determinant and as an (n × n)-determinant. The latter was first obtained by I Kostov. We show that the two determinants are equal, as expected from the fact that they are partition functions of the same object, that each is a discrete KP τ-function, and, recalling that these determinants represent tree-level structure constants in $ \mathcal{N} = 4\;{\text{SYM}} $, we show that introducing 1-loop corrections, as proposed by N Gromov and P Vieira, preserves the determinant structure. © SISSA 2012
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