Modular invariance of the thermo-partition function and global phase structure of the heterotic string

1987 ◽  
Vol 36 (4) ◽  
pp. 1184-1192 ◽  
Author(s):  
K. H. O’Brien ◽  
C.-I Tan
Keyword(s):  
Partition Function ◽  
Phase Structure ◽  
Heterotic String ◽  
Modular Invariance

scholarly journals Multiple phases in a generalized Gross-Witten-Wadia matrix model

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Jorge G. Russo ◽  
Miguel Tierz
Keyword(s):  
Partition Function ◽  
Matrix Models ◽  
Characteristic Polynomial ◽  
Matrix Model ◽  
Phase Structure ◽  
Unitary Matrix ◽  
Two Dimensional ◽  
Toeplitz Determinants ◽  
Dimensional Parameter ◽  
Planar Limit

Abstract We study a unitary matrix model of the Gross-Witten-Wadia type, extended with the addition of characteristic polynomial insertions. The model interpolates between solvable unitary matrix models and is the unitary counterpart of a deformed Cauchy ensemble. Exact formulas for the partition function and Wilson loops are given in terms of Toeplitz determinants and minors and large N results are obtained by using Szegö theorem with a Fisher-Hartwig singularity. In the large N (planar) limit with two scaled couplings, the theory exhibits a surprisingly intricate phase structure in the two-dimensional parameter space.

A NOTE ON DISCRETE SYMMETRIES IN TOROIDAL COMPACTIFICATIONS OF STRINGS

1990 ◽  
Vol 05 (22) ◽  
pp. 1779-1785 ◽  
Author(s):  
M. A. R. OSORIO
Keyword(s):  
Partition Function ◽  
Discrete Symmetries ◽  
Modular Invariance ◽  
World Sheet ◽  
Toroidal Compactifications ◽  
Instanton Contribution

In this paper we look for discrete invariances of the partition function in toroidal compactifications of strings. We show that besides world-sheet modular invariance, the partition function is invariant under GL (2d, ℤ) transformations ( GL (2d + 16, ℤ) when Wilson lines are present) acting upon the instanton contribution.

LEVEL-ONE SU(N) WZNW MODELS ON HIGHER-GENUS RIEMANN SURFACES

1993 ◽  
Vol 08 (17) ◽  
pp. 2955-2972 ◽  
Author(s):  
M. ALIMOHAMMADI ◽  
H. ARFAEI
Keyword(s):  
Partition Function ◽  
Simple Form ◽  
Riemann Surfaces ◽  
Theta Functions ◽  
Modular Invariance ◽  
Fusion Rules ◽  
Group Manifold ◽  
Special Cases ◽  
Wznw Model ◽  
Higher Genus

Using factorization properties and fusion rules, we find the higher-genus partition function and two-point correlators for the SU (N)1 WZNW model. The result has simple form in terms of higher-genus theta functions on the group manifold. The previously known results of SU (2)1 and SU (3)1 are also obtained as special cases. This method, combined with other considerations such as modular invariance, can be extended to the nonsimply laced groups and higher-level WZNW models.

scholarly journals Lessons from the Ramond sector

2020 ◽  
Vol 9 (5) ◽  
Author(s):  
Nathan Benjamin ◽  
Ying-Hsuan Lin
Keyword(s):  
Partition Function ◽  
Field Theories ◽  
Partition Functions ◽  
Modular Invariance ◽  
Conformal Field Theories ◽  
Modular Functions ◽  
Conformal Field ◽  
Underlying Theory ◽  
Rule Out

We revisit the consistency of torus partition functions in (1+1)d fermionic conformal field theories, combining old ingredients of modular invariance/covariance with a modernized understanding of bosonization/fermionization dualities. Various lessons can be learned by simply examining the oft-ignored Ramond sector. For several extremal/kinky modular functions in the bootstrap literature, we can either rule out or identify the underlying theory. We also revisit the N = 1 Maloney-Witten partition function by calculating the spectrum in the Ramond sector, and further extending it to include the modular sum of seed Ramond characters. Finally, we perform the full N = 1 RNS modular bootstrap and obtain new universal results on the existence of relevant deformations preserving different amounts of supersymmetry.

scholarly journals S-DUALITY AND THE ENTROPY OF BLACK HOLES IN HETEROTIC STRING THEORY

1996 ◽  
Vol 11 (39n40) ◽  
pp. 3103-3111 ◽  
Author(s):  
AMIT GHOSH ◽  
JNANADEVA MAHARANA
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Partition Function ◽  
Heterotic String ◽  
Heterotic String Theory ◽  
Charged Black Holes ◽  
Duality Transformations ◽  
Extremal Limit ◽  
Electrically Charged ◽  
Black Hole Solutions

Four-dimensional heterotic string effective action is known to admit non-rotating electrically and magnetically charged black hole solutions. The partition function and entropy is computed for electrically charged black holes and is vanishing in some extremal limit. For the magnetically charged black holes the entropy is also argued to be vanishing in the same extremal limit when these black hole solutions are related by S-duality transformations.

scholarly journals ON THE SPECTRUM, NO-GHOST THEOREM AND MODULAR INVARIANCE OF W3 STRINGS

1993 ◽  
Vol 08 (17) ◽  
pp. 2875-2893 ◽  
Author(s):  
PETER WEST
Keyword(s):  
Ising Model ◽  
Partition Function ◽  
Ghost Number ◽  
Modular Invariance ◽  
Modular Invariant

A spectrum-generating algebra is constructed and used to find all the physical states of the W3 string with standard ghost number. These states are shown to have positive norm and their partition function is found to involve the Ising model characters corresponding to the weights 0 and 1/16. The theory is found to be modular invariant if, in addition, one includes states that correspond to the Ising character of weight 1/2. It is shown that these additional states are indeed contained in the cohomology of Q.

scholarly journals On the spectrum of pure higher spin gravity

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Luis F. Alday ◽  
Jin-Beom Bae ◽  
Nathan Benjamin ◽  
Carmen Jorge-Diaz
Keyword(s):  
Black Hole ◽  
Partition Function ◽  
Path Integral ◽  
Higher Spin Gravity ◽  
Central Charge ◽  
Modular Invariance ◽  
Light Spectrum ◽  
Negative Norm ◽  
Deficit Angle ◽  
Higher Spin

Abstract We study the spectrum of pure massless higher spin theories in AdS3. The light spectrum is given by a tower of massless particles of spin s = 2, ⋯ , N and their multi-particles states. Their contribution to the torus partition function organises into the vacuum character of the $$ {\mathcal{W}}_N $$ W N algebra. Modular invariance puts constraints on the heavy spectrum of the theory, and in particular leads to negative norm states, which would be inconsistent with unitarity. This negativity can be cured by including additional light states, below the black hole threshold but whose mass grows with the central charge. We show that these states can be interpreted as conical defects with deficit angle 2π(1 − 1/M). Unitarity allows the inclusion of such defects into the path integral provided M ≥ N.

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