19,202 research outputs found

### Melting Crystal, Quantum Torus and Toda Hierarchy

Searching for the integrable structures of supersymmetric gauge theories and
topological strings, we study melting crystal, which is known as random plane
partition, from the viewpoint of integrable systems. We show that a series of
partition functions of melting crystals gives rise to a tau function of the
one-dimensional Toda hierarchy, where the models are defined by adding suitable
potentials, endowed with a series of coupling constants, to the standard
statistical weight. These potentials can be converted to a commutative
sub-algebra of quantum torus Lie algebra. This perspective reveals a remarkable
connection between random plane partition and quantum torus Lie algebra, and
substantially enables to prove the statement. Based on the result, we briefly
argue the integrable structures of five-dimensional $\mathcal{N}=1$
supersymmetric gauge theories and $A$-model topological strings. The
aforementioned potentials correspond to gauge theory observables analogous to
the Wilson loops, and thereby the partition functions are translated in the
gauge theory to generating functions of their correlators. In topological
strings, we particularly comment on a possibility of topology change caused by
condensation of these observables, giving a simple example.Comment: Final version to be published in Commun. Math. Phys. . A new section
is added and devoted to Conclusion and discussion, where, in particular, a
possible relation with the generating function of the absolute Gromov-Witten
invariants on CP^1 is commented. Two references are added. Typos are
corrected. 32 pages. 4 figure

### Canonical treatment of two dimensional gravity as an anomalous gauge theory

The extended phase space method of Batalin, Fradkin and Vilkovisky is applied
to formulate two dimensional gravity in a general class of gauges. A BRST
formulation of the light-cone gauge is presented to reveal the relationship
between the BRST symmetry and the origin of $SL(2,R)$ current algebra. From the
same principle we derive the conformal gauge action suggested by David, Distler
and Kawai.Comment: 11 pages, KANAZAWA-92-1

### Unified picture of Q-balls and boson stars via catastrophe theory

We make an analysis of Q-balls and boson stars using catastrophe theory, as
an extension of the previous work on Q-balls in flat spacetime. We adopt the
potential $V_3(\phi)={m^2\over2}\phi^2-\mu\phi^3+\lambda\phi^4$ for Q-balls and
that with $\mu =0$ for boson stars. For solutions with $|g^{rr}-1|\sim 1$ at
its peak, stability of Q-balls has been lost regardless of the potential
parameters. As a result, phase relations, such as a Q-ball charge versus a
total Hamiltonian energy, approach those of boson stars, which tell us an
unified picture of Q-balls and boson stars.Comment: 10 pages, 13 figure

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