COUNTING BPS STATES IN E-STRING THEORY

2013 ◽  
Vol 21 ◽  
pp. 116-125
Author(s):  
KAZUHIRO SAKAI
Keyword(s):  
String Theory ◽  
Partition Function ◽  
Four Dimensions ◽  
Anomaly Equation ◽  
Bps States

We find a Nekrasov-type expression for the Seiberg–Witten prepotential for the six-dimensional non-critical E8 string theory toroidally compactified down to four dimensions. The prepotential represents the BPS partition function of the E8 strings wound around one of the circles of the toroidal compactification with general winding numbers and momenta. We show that our expression exhibits expected modular properties. In particular, we prove that it obeys the modular anomaly equation known to be satisfied by the prepotential.

scholarly journals Refinement and modularity of immortal dyons

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sergei Alexandrov ◽  
Suresh Nampuri
Keyword(s):  
String Theory ◽  
Generating Functions ◽  
Duality Group ◽  
Holomorphic Anomaly ◽  
String Compactifications ◽  
Holomorphic Anomaly Equation ◽  
Anomaly Equation ◽  
Universal Structure ◽  
Bps States ◽  
Torsion Invariant

Abstract Extending recent results in $$ \mathcal{N} $$ N = 2 string compactifications, we propose that the holomorphic anomaly equation satisfied by the modular completions of the generating functions of refined BPS indices has a universal structure independent of the number $$ \mathcal{N} $$ N of supersymmetries. We show that this equation allows to recover all known results about modularity (under SL(2, ℤ) duality group) of BPS states in $$ \mathcal{N} $$ N = 4 string theory. In particular, we reproduce the holomorphic anomaly characterizing the mock modular behavior of quarter-BPS dyons and generalize it to the case of non-trivial torsion invariant.

scholarly journals On the quantization of Seiberg-Witten geometry

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nathan Haouzi ◽  
Jihwan Oh
Keyword(s):  
Gauge Theory ◽  
String Theory ◽  
Partition Function ◽  
Flat Space ◽  
Matter Content ◽  
Gauge Groups ◽  
Space Limit ◽  
Two Parameters ◽  
Double Quantization ◽  
Quantization Parameters

Abstract We propose a double quantization of four-dimensional $$ \mathcal{N} $$ N = 2 Seiberg-Witten geometry, for all classical gauge groups and a wide variety of matter content. This can be understood as a set of certain non-perturbative Schwinger-Dyson identities, following the program initiated by Nekrasov [1]. The construction relies on the computation of the instanton partition function of the gauge theory on the so-called Ω-background on ℝ4, in the presence of half-BPS codimension 4 defects. The two quantization parameters are identified as the two parameters of this background. The Seiberg-Witten curve of each theory is recovered in the flat space limit. Whenever possible, we motivate our construction from type IIA string theory.

scholarly journals Partition function and open/closed string duality in type IIA string theory on a pp-wave

2003 ◽  
Vol 669 (1-2) ◽  
pp. 78-102 ◽  
Author(s):  
Hyeonjoon Shin ◽  
Katsuyuki Sugiyama ◽  
Kentaroh Yoshida
Keyword(s):  
String Theory ◽  
Partition Function ◽  
String Duality ◽  
Closed String ◽  
Pp Wave

scholarly journals Quiver matrix model of ADHM type and BPS state counting in diverse dimensions

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Hiroaki Kanno
Keyword(s):  
Partition Function ◽  
Matrix Model ◽  
Characteristic Property ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Torus Action ◽  
Localization Theorem ◽  
Counting Problem ◽  
Expectation Value ◽  
Four Dimensions

Abstract We review the problem of Bogomol’nyi–Prasad–Sommerfield (BPS) state counting described by the generalized quiver matrix model of Atiyah–Drinfield–Hitchin–Manin type. In four dimensions the generating function of the counting gives the Nekrasov partition function, and we obtain a generalization in higher dimensions. By the localization theorem, the partition function is given by the sum of contributions from the fixed points of the torus action, which are labeled by partitions, plane partitions and solid partitions. The measure or the Boltzmann weight of the path integral can take the form of the plethystic exponential. Remarkably, after integration the partition function or the vacuum expectation value is again expressed in plethystic form. We regard it as a characteristic property of the BPS state counting problem, which is closely related to the integrability.

Evolutionary string theory

2007 ◽  
Vol 30 (4) ◽  
pp. 369-370
Author(s):  
Zen Faulkes ◽  
Anita Davelos Baines
Keyword(s):  
String Theory ◽  
Research Program ◽  
Extra Dimensions ◽  
Evolutionary Biology ◽  
Four Dimensions ◽  
Productive Research

AbstractEvolution in Four Dimensions claims that epigenetic, behavioral, and symbolic inheritance systems should be considered equal partners to genetics in evolutionary biology. The evidence for, and applicable scope of, these additional inheritance systems is limited, particularly with regard to areas involving learning. It is unclear how including these extra dimensions in mainstream evolutionary thinking translates into testable hypotheses for a productive research program.

scholarly journals TOPOLOGICAL LATTICE MODELS IN FOUR DIMENSIONS

1992 ◽  
Vol 07 (30) ◽  
pp. 2799-2810 ◽  
Author(s):  
HIROSI OOGURI
Keyword(s):  
Partition Function ◽  
Piecewise Linear ◽  
Lattice Models ◽  
Closed Surface ◽  
Statistical Weight ◽  
Four Dimensions ◽  
Angular Momenta ◽  
Topological Lattice ◽  
Wilson Operator ◽  
Dimensional Version

We define a lattice statistical model on a triangulated manifold in four dimensions associated to a group G. When G= SU (2), the statistical weight is constructed from the 15j-symbol as well as the 6j-symbol for recombination of angular momenta, and the model may be regarded as the four-dimensional version of the Ponzano-Regge model. We show that the partition function of the model is invariant under the Alexander moves of the simplicial complex, thus it depends only on the piecewise linear topology of the manifold. For an orientable manifold, the model is related to the so-called BF model. The q-analog of the model is also constructed, and it is argued that its partition function is invariant under the Alexander moves. It is discussed how to realize the 't Hooft operator in these models associated to a closed surface in four dimensions as well as the Wilson operator associated to a closed loop. Correlation functions of these operators in the q-deformed version of the model would define a new type of invariants of knots and links in four dimensions.

scholarly journals Stable non-BPS states in string theory

1998 ◽  
Vol 1998 (06) ◽  
pp. 007-007 ◽  
Author(s):  
Ashoke Sen
Keyword(s):  
String Theory ◽  
Bps States

scholarly journals Non-perturbative Nekrasov partition function from string theory

2014 ◽  
Vol 880 ◽  
pp. 87-108 ◽  
Author(s):  
I. Antoniadis ◽  
I. Florakis ◽  
S. Hohenegger ◽  
K.S. Narain ◽  
A. Zein Assi
Keyword(s):  
String Theory ◽  
Partition Function

scholarly journals TWO-DIMENSIONAL YANG-MILLS THEORIES ARE STRING THEORIES

1993 ◽  
Vol 08 (23) ◽  
pp. 2223-2235 ◽  
Author(s):  
STEPHEN G. NACULICH ◽  
HAROLD A. RIGGS ◽  
HOWARD J. SCHNITZER
Keyword(s):  
String Theory ◽  
Partition Function ◽  
Arbitrary Number ◽  
Closed String ◽  
Two Dimensional ◽  
Branched Covers ◽  
Yang Mills ◽  
String Worldsheet ◽  
String Theories

We show that two-dimensional SO (N) and Sp (N) Yang-Mills theories without fermions can be interpreted as closed string theories. The terms in the 1/N expansion of the partition function on an orientable or nonorientable manifold ℳ can be associated with maps from a string worldsheet onto ℳ. These maps are unbranched and branched covers of ℳ with an arbitrary number of infinitesimal worldsheet cross-caps mapped to points in ℳ. These string theories differ from SU (N) Yang-Mills string theory in that they involve odd powers of 1/N and require both orientable and nonorientable worldsheets.

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