Exponential Networks and Representations of Quivers
- Eager, Richard et al
- arXiv:1611.06177
 | Local structure of BPS trajectories near an $ij$-branch point. |
 | Local structure of BPS trajectories near an $ij$-branch point. |
 | Birth of an $(ik)$-trajectory at the intersection of an $(ij)$- and a $(jk)$-trajectory. |
 | Birth of an $(ik)$-trajectory at the intersection of an $(ij)$- and a $(jk)$-trajectory. |
 | T-duality picture of bound state formation. |
 | T-duality picture of bound state formation. |
 | Monopole of charge $(1,0)$. |
 | Monopole of charge $(1,0)$. |
 | Dyon of charge $(0,1)$. |
 | Dyon of charge $(0,1)$. |
 | A bound state with charge $(2,1)$. |
 | A bound state with charge $(2,1)$. |
 | Closed loops with charge $(1,1)$. |
 | Closed loops with charge $(1,1)$. |
 | $(3,2)$ bound state and its corresponding quiver representation. |
 | $(3,2)$ bound state and its corresponding quiver representation. |
 | Holomorphic disk bounded by five Lagrangians. |
 | Holomorphic disk bounded by five Lagrangians. |
 | D$0$-brane around a puncture. |
 | D$0$-brane around a puncture. |
 | Local structure of BPS trajectories near a $+-$ branch point. |
 | Local structure of BPS trajectories near a $+-$ branch point. |
 | Resolution of junctions with multiplicity. |
 | Resolution of junctions with multiplicity. |
 | $\C^3$ |
 | $\C^3$ |
 | Resolved conifold |
 | Resolved conifold |
 | local $\CP^2$ |
 | local $\CP^2$ |
 | $\Dtwobar$ + D0 brane. |
 | $\Dtwobar$ + D0 brane. |
 | D2 brane. |
 | D2 brane. |
 | The two basic states for the conifold. |
 | The two basic states for the conifold. |
 | Rendering on the mirror curve of the two basic states on the resolved conifold. |
 | Rendering on the mirror curve of the two basic states on the resolved conifold. |
 | $\Dtwobar + 2{\rm D}0$ or brane $(2,1)$ at $|Q|>1$. |
 | $\Dtwobar + 2{\rm D}0$ or brane $(2,1)$ at $|Q|>1$. |
 | Brane $(2,1)$ at $|Q|<1$. |
 | Brane $(2,1)$ at $|Q|<1$. |
 | The D0 brane $(1,1)$ at $|Q|<1$. |
 | The D0 brane $(1,1)$ at $|Q|<1$. |
 | Generic finite web for the D0-brane on the resolved conifold. |
 | Generic finite web for the D0-brane on the resolved conifold. |
 | Moduli of D$0$-brane on the resolved conifold. Networks plotted in a variable such that the $x=\infty$ puncture lies at finite distance. |
 | Moduli of D$0$-brane on the resolved conifold. Networks plotted in a variable such that the $x=\infty$ puncture lies at finite distance. |
 | Two fixed points for the D0 brane $(1,1)$ at $|Q|>1$. |
 | Two fixed points for the D0 brane $(1,1)$ at $|Q|>1$. |
 | Spectral network at $Q=-1$, on the line of marginal stability. |
 | Spectral network at $Q=-1$, on the line of marginal stability. |
 | The three fractional branes near the orbifold point and the bifundamental fields corresponding to their intersection points. Note that the fractional branes all occur at different phases.Central charges of the fractional branes at $\psi = -\frac{1}{6}.$ |
 | The three fractional branes near the orbifold point and the bifundamental fields corresponding to their intersection points. Note that the fractional branes all occur at different phases.Central charges of the fractional branes at $\psi = -\frac{1}{6}.$ |
 | Resolve by a 1:1 strand ($++$ or $--$). |
 | Resolve by a 1:1 strand ($++$ or $--$). |
 | Detach from bottom branch point. |
 | Detach from bottom branch point. |
 | Resolve by a 2:1 strand. |
 | Resolve by a 2:1 strand. |
 | Resolve by a ($++$) or ($--$) strand and detach from bottom branch point. |
 | Resolve by a ($++$) or ($--$) strand and detach from bottom branch point. |
 | Notations for 1:1 collision. |
 | Notations for 1:1 collision. |
 | Notations for 2:1 collision. |
 | Notations for 2:1 collision. |
 | The finite web for the unique (fixed) point in $K_3(1,3)$. |
 | The finite web for the unique (fixed) point in $K_3(1,3)$. |
 | A tree module for a dimension $(2,5)$ representation.A finite web for dimension $(2,5)$ representation.A different tree module for a dimension $(2,5)$ representation. |
 | A tree module for a dimension $(2,5)$ representation.A finite web for dimension $(2,5)$ representation.A different tree module for a dimension $(2,5)$ representation. |
 | $(ij)_n$ notation illustrated on the finite web for the (2,5) representation of the Kronecker-3 quiver. |
 | $(ij)_n$ notation illustrated on the finite web for the (2,5) representation of the Kronecker-3 quiver. |
 | Tree module notation illustrated on the finite web for the (2,5) representation of the Kronecker-3 quiver. |
 | Tree module notation illustrated on the finite web for the (2,5) representation of the Kronecker-3 quiver. |
 | The finite web for the dimension $(3,8)$ representation. |
 | The finite web for the dimension $(3,8)$ representation. |
 | Network at $\vartheta=0$ at a point in moduli space where the D4- and D0-brane coexist. The blue segment is the D4-brane. The inner loop, along with the outer finite web for either choice of $(++)$ or $(--)$, constitute the three fixed points of the D0-brane. |
 | Network at $\vartheta=0$ at a point in moduli space where the D4- and D0-brane coexist. The blue segment is the D4-brane. The inner loop, along with the outer finite web for either choice of $(++)$ or $(--)$, constitute the three fixed points of the D0-brane. |
 | Parametric dependence of the periods along the negative $\psi$-axis. |
 | Parametric dependence of the periods along the negative $\psi$-axis. |
 | Wall of marginal stability |
 | Wall of marginal stability |
 | $\psi<\psi_{critical}$ |
 | $\psi<\psi_{critical}$ |
 | $\psi=\psi_{critical}$ |
 | $\psi=\psi_{critical}$ |
 | $\psi>\psi_{critical}$ |
 | $\psi>\psi_{critical}$ |
 | Network at $\vartheta=0$ on $\complex^3$. Compare with Figure \ref{fig:P2LargeVolume}. |
 | Network at $\vartheta=0$ on $\complex^3$. Compare with Figure \ref{fig:P2LargeVolume}. |
 | Sample network for the $\C^3$ geometry. |
 | Sample network for the $\C^3$ geometry. |
 | Rendering of the branes on the mirror curve for $\complex^3$. |
 | Rendering of the branes on the mirror curve for $\complex^3$. |
 | The D0 brane at framing where the mirror curve is cubic in $y$. |
 | The D0 brane at framing where the mirror curve is cubic in $y$. |
 | Moduli of D$0$-brane on $\C^3$. |
 | Moduli of D$0$-brane on $\C^3$. |
 | D4 brane at non-zero B-field. |
 | D4 brane at non-zero B-field. |
 | Bound state of the D4- with the D0 brane at non-zero B-field. |
 | Bound state of the D4- with the D0 brane at non-zero B-field. |
 | Bound state of the D4 brane with two D0 branes. |
 | Bound state of the D4 brane with two D0 branes. |
 | D4 + $3$D0, one $(+-)_1$ street corresponding to the partition (2,1). |
 | D4 + $3$D0, one $(+-)_1$ street corresponding to the partition (2,1). |
 | D4 $+$ $3$D0, two $(++)/(--)$ streets corresponding to the partitions (3) and (1,1,1). |
 | D4 $+$ $3$D0, two $(++)/(--)$ streets corresponding to the partitions (3) and (1,1,1). |
 | D4 + $4$D0, corresponding to the partitions (4) and (1,1,1,1). |
 | D4 + $4$D0, corresponding to the partitions (4) and (1,1,1,1). |
 | D4 + $4$D0, corresponding to the partition (2,2). |
 | D4 + $4$D0, corresponding to the partition (2,2). |
 | D4 + $4$D0, ``L" partition. |
 | D4 + $4$D0, ``L" partition. |