Landscape

Select a theory SU(2): 4 fund + 4 anti-fund (not completed) SU(2): 1 Adj + 1 fund + 1 anti-fund SU(2): 1 Adj + 2 fund + 2 anti-fund (not completed) SU(2): 1 Adj + 3 fund + 3 anti-fund (not completed) SU(2): 2 Adj SU(2): 2 Adj + 1 fund + 1 anti-fund SU(3): 1 Adj + 1 fund + 1 anti-fund SU(3): 1 Adj + 2 fund + 2 anti-fund (not completed) SU(5): 2 rank-2 symm + (conj.) SU(5): 1 rank-2 symm + 1 rank-2 anti-symm + (conj.) SU(5): 1 rank-2 symm + 1 rank-2 anti-symm + 1 fund + (conj.) (not completed) SU(5): 1 rank-2 symm + 1 rank-2 anti-symm + 2 conj. of rank-2 anti-symm + 8 anti-fund (not completed) SU(5): 1 rank-2 symm + 1 rank-2 anti-symm + 2 conj. of rank-2 anti-symm + 1 fund + 9 anti-fund (not completed) SU(5): 1 Adj + 1 rank-2 symm + 1 conj. of rank-2 symm SU(5): 1 Adj + 1 rank-2 symm + 1 conj. of rank-2 symm + 1 fund + 1 anti-fund SU(5): 1 Adj + 1 rank-2 symm + 1 conj. of rank-2 anti-symm + 8 anti-fund (not completed) SU(5): 1 Adj + 1 rank-2 anti-symm + 1 conj. of rank-2 anti-symm SU(5): 1 Adj + 1 rank-2 anti-symm + 1 conj. of rank-2 anti-symm + 1 fund + 1 anti-fund (not completed) SU(5): 1 rank-2 symm + 2 rank-2 anti-symm + (conj.) (not completed) SU(5): 1 rank-2 symm + 2 rank-2 anti-symm + 1 fund + (conj.) (not completed) SU(5): 3 rank-2 anti-symm + (conj.) (not completed) SU(5): 3 rank-2 anti-symm + 1 fund + (conj.) (not completed) SU(5): 2 Adj + 1 anti-symm + 1 conj. of rank-2 anti-symm (not completed) SU(5): 2 Adj + 1 anti-symm + 1 conj. of rank-2 anti-symm + 1 fund + 1 anti-fund (not completed) SU(6): 2 rank-2 symm + (conj.) SU(6): 2 rank-2 symm + 1 fund + (conj.) SU(6): 1 rank-2 symm + 1 rank-2 anti-symm + (conj.) SU(6): 1 rank-2 symm + 1 rank-2 anti-symm + 2 conj. of rank-2 anti-symm + 1 fund + 9 anti-fund (not completed) SU(6): 1 Adj + 1 rank-2 symm + 1 conj. of rank-2 symm SU(6): 1 Adj + 1 rank-2 symm + 1 conj. of rank-2 anti-symm + 1 fund + 9 anti-fund (not completed) SU(7): 1 rank-2 symm + 2 conj. of rank-2 symm + 1 anti-symm + 8 fund (not completed) SU(7): 2 rank-2 symm + 1 fund + (conj.) (not completed) SU(8): 1 rank-2 symm + 2 conj. of rank-2 symm + 1 anti-symm + 9 fund + 1 anti-fund (not completed) SU(9): 2 rank-2 symm + 2 conj. of rank-2 anti-symm + 16 anti-fund (not completed) SU(9): 2 rank-2 symm + (conj.) (not completed) SU(9): 2 rank-2 symm + 1 fund (conj.) (not completed) SU(10): 2 rank-2 symm + 2 conj. of rank-2 anti-symm + 1 fund + 17 anti-fund (not completed) SO(5): 5 vector (not completed) SO(5): 1 Adj + 1 vector SO(5): 1 Adj + 2 vector SO(5): 1 rank-2 symm SO(5): 1 rank-2 symm + 1 vector SO(5): 1 rank-2 symm + 2 vector Sp(2): 1 Adj + 2 fund Sp(2): 1 14 + 2 fund Sp(2): 2 Adj Sp(2): 1 Adj + 2 rank-2 anti-symm + 8 fund (not completed) G2: 1 Adj + 1 fund E[USp(6)] (not completed) All theories Data used in arXiv:2408.02953

$a$ =

$c$ =

$\leq a \leq$

$\leq c \leq$

id =

Check if you want only theories with rational charges.

Chosen Fixed Point

Here is the data for the chosen fixed point.
$F_{UV}$ represents the flavor symmetries in the UV Lagrangian, and $F_{IR}$ represents the flavor symmetries in the IR. $F_{UV}$ and $F_{IR}$ can differ due to accidental symmetry enhancement.
The number of marginal operators, $n_{marginal}$, minus the dimension of flavor symmetries in IR, $|F_{IR}|$, corresponds to the coefficient of $t^6$ in the superconformal index.

#	Theory	Superpotential	Central charge $a$	Central charge $c$	Ratio $a/c$	Matter field: $R$-charge	U(1) part of $F_{UV}$	Rank of $F_{UV}$	Rational
61193	SU3adj1nf2	${}\phi_{1}^{4}$ + ${ }q_{1}\tilde{q}_{1}X_{1}$ + ${ }q_{2}\tilde{q}_{1}X_{2}$ + ${ }q_{1}\tilde{q}_{2}X_{3}$ + ${ }q_{2}\tilde{q}_{2}X_{4}$ + ${ }M_{1}\phi_{1}q_{2}\tilde{q}_{2}$ + ${ }M_{2}\phi_{1}q_{1}^{2}q_{2}$ + ${ }M_{3}\phi_{1}\tilde{q}_{1}^{2}\tilde{q}_{2}$ + ${ }M_{4}\phi_{1}q_{1}q_{2}^{2}$	1.0253	1.2616	0.8127	[X:[1.5285, 1.4917, 1.5083, 1.4715], M:[0.9715, 0.7559, 0.7725, 0.7192], q:[0.2358, 0.2725], qb:[0.2358, 0.2559], phi:[0.5]]	[X:[[0, 0, -1], [0, -1, 0], [0, 1, 0], [0, 0, 1]], M:[[0, 0, 1], [3, 2, 1], [-3, -2, -2], [3, 1, 2]], q:[[-1, -1, 0], [-1, 0, -1]], qb:[[1, 1, 1], [1, 0, 0]], phi:[[0, 0, 0]]]	3

Relevant Operators	Marginal Operators	$n_{marginal}$$-$$|F_{IR}|$	Superconformal Index	Refined index
${}M_{4}$, ${ }M_{2}$, ${ }M_{3}$, ${ }M_{1}$, ${ }\phi_{1}q_{1}\tilde{q}_{1}$, ${ }\phi_{1}q_{1}\tilde{q}_{2}$, ${ }\phi_{1}^{2}$, ${ }\phi_{1}q_{2}\tilde{q}_{1}$, ${ }\phi_{1}\tilde{q}_{1}\tilde{q}_{2}^{2}$, ${ }M_{4}^{2}$, ${ }\phi_{1}^{2}q_{1}\tilde{q}_{1}$, ${ }X_{4}$, ${ }M_{2}M_{4}$, ${ }M_{3}M_{4}$, ${ }\phi_{1}^{2}q_{1}\tilde{q}_{2}$, ${ }X_{2}$, ${ }\phi_{1}^{3}$, ${ }\phi_{1}^{2}q_{2}\tilde{q}_{1}$, ${ }X_{3}$, ${ }M_{2}^{2}$, ${ }M_{2}M_{3}$, ${ }\phi_{1}^{2}q_{2}\tilde{q}_{2}$, ${ }X_{1}$, ${ }M_{3}^{2}$, ${ }M_{1}M_{4}$, ${ }M_{4}\phi_{1}q_{1}\tilde{q}_{1}$, ${ }M_{4}\phi_{1}q_{1}\tilde{q}_{2}$, ${ }M_{4}\phi_{1}^{2}$, ${ }M_{1}M_{2}$, ${ }M_{2}\phi_{1}q_{1}\tilde{q}_{1}$, ${ }M_{4}\phi_{1}q_{2}\tilde{q}_{1}$, ${ }\phi_{1}^{2}\tilde{q}_{1}^{2}\tilde{q}_{2}$, ${ }M_{1}M_{3}$, ${ }\phi_{1}^{2}q_{1}^{2}q_{2}$, ${ }M_{3}\phi_{1}q_{1}\tilde{q}_{1}$, ${ }M_{2}\phi_{1}q_{1}\tilde{q}_{2}$, ${ }\phi_{1}^{2}\tilde{q}_{1}\tilde{q}_{2}^{2}$, ${ }M_{2}\phi_{1}^{2}$, ${ }M_{3}\phi_{1}q_{1}\tilde{q}_{2}$, ${ }M_{2}\phi_{1}q_{2}\tilde{q}_{1}$, ${ }M_{3}\phi_{1}^{2}$, ${ }\phi_{1}^{2}q_{1}q_{2}^{2}$, ${ }M_{3}\phi_{1}q_{2}\tilde{q}_{1}$, ${ }M_{1}^{2}$, ${ }M_{1}\phi_{1}q_{1}\tilde{q}_{1}$, ${ }\phi_{1}^{2}q_{1}^{2}\tilde{q}_{1}^{2}$, ${ }M_{1}\phi_{1}q_{1}\tilde{q}_{2}$, ${ }\phi_{1}^{2}q_{1}^{2}\tilde{q}_{1}\tilde{q}_{2}$, ${ }M_{4}\phi_{1}\tilde{q}_{1}\tilde{q}_{2}^{2}$, ${ }M_{1}\phi_{1}^{2}$, ${ }M_{1}\phi_{1}q_{2}\tilde{q}_{1}$, ${ }\phi_{1}^{2}q_{1}q_{2}\tilde{q}_{1}^{2}$, ${ }\phi_{1}^{2}q_{1}^{2}\tilde{q}_{2}^{2}$	${}$	-3	t^2.16 + t^2.27 + t^2.32 + 2*t^2.91 + t^2.98 + t^3. + t^3.02 + t^3.74 + t^4.32 + 2*t^4.41 + t^4.43 + 3*t^4.48 + t^4.5 + 2*t^4.52 + t^4.54 + 3*t^4.59 + t^4.64 + 2*t^5.07 + t^5.13 + t^5.16 + 4*t^5.18 + 3*t^5.23 + 2*t^5.24 + t^5.27 + 2*t^5.29 + t^5.32 + 2*t^5.34 + 3*t^5.83 + t^5.89 + t^5.9 + t^5.91 + t^5.94 + t^5.95 - 3*t^6. + t^6.01 + t^6.05 - t^6.09 - t^6.11 + t^6.47 + 2*t^6.57 + t^6.58 + 2*t^6.62 + 3*t^6.63 + t^6.66 + 4*t^6.68 + t^6.69 + t^6.72 + 2*t^6.73 + 6*t^6.74 - 2*t^6.76 + 5*t^6.79 + 2*t^6.8 - t^6.82 + 2*t^6.84 + 3*t^6.85 + 3*t^6.9 + 2*t^6.95 + 2*t^7.23 + t^7.29 + t^7.32 + 4*t^7.33 + 4*t^7.34 + 8*t^7.39 + 2*t^7.4 + 2*t^7.41 + t^7.43 + 5*t^7.44 + 7*t^7.45 + 2*t^7.48 + t^7.49 + 11*t^7.5 + 2*t^7.51 + t^7.52 + t^7.54 + 5*t^7.55 + 4*t^7.56 + t^7.59 + 4*t^7.61 + t^7.64 + 2*t^7.66 + 3*t^7.99 + t^8.05 + t^8.06 + t^8.07 + 4*t^8.1 + t^8.11 - 2*t^8.12 + 3*t^8.15 - t^8.16 + t^8.17 + t^8.21 + 2*t^8.22 - t^8.24 - 4*t^8.27 + t^8.28 - t^8.3 - 5*t^8.32 - t^8.34 - t^8.35 - t^8.38 - t^8.4 - 3*t^8.43 - t^8.45 + t^8.63 + 2*t^8.73 + 5*t^8.74 + 2*t^8.78 + 3*t^8.79 + t^8.8 + t^8.82 + 4*t^8.83 + 4*t^8.84 + 2*t^8.85 + t^8.86 + t^8.88 + 5*t^8.89 + 6*t^8.9 - 12*t^8.91 + 2*t^8.93 + 3*t^8.94 + 10*t^8.95 + 3*t^8.96 - 7*t^8.98 + 2*t^8.99 - t^4.5/y - t^6./y - t^6.66/y - t^6.77/y - t^6.82/y - t^7.41/y + t^7.43/y + t^7.48/y + t^7.5/y + (2*t^7.59)/y + (2*t^8.07)/y + t^8.13/y + (4*t^8.18)/y + (3*t^8.23)/y + t^8.24/y + (2*t^8.29)/y + (2*t^8.34)/y - t^8.82/y + t^8.83/y + (2*t^8.89)/y + t^8.9/y - t^8.91/y - t^8.93/y + (2*t^8.94)/y - (2*t^8.98)/y - t^4.5*y - t^6.*y - t^6.66*y - t^6.77*y - t^6.82*y - t^7.41*y + t^7.43*y + t^7.48*y + t^7.5*y + 2*t^7.59*y + 2*t^8.07*y + t^8.13*y + 4*t^8.18*y + 3*t^8.23*y + t^8.24*y + 2*t^8.29*y + 2*t^8.34*y - t^8.82*y + t^8.83*y + 2*t^8.89*y + t^8.9*y - t^8.91*y - t^8.93*y + 2*t^8.94*y - 2*t^8.98*y	g1^3*g2*g3^2*t^2.16 + g1^3*g2^2*g3*t^2.27 + t^2.32/(g1^3*g2^2*g3^2) + 2*g3*t^2.91 + t^2.98/g2 + t^3. + g2*t^3.02 + g1^3*g2*g3*t^3.74 + g1^6*g2^2*g3^4*t^4.32 + 2*g3*t^4.41 + g1^6*g2^3*g3^3*t^4.43 + (3*t^4.48)/g2 + t^4.5 + 2*g2*t^4.52 + g1^6*g2^4*g3^2*t^4.54 + (3*t^4.59)/g3 + t^4.64/(g1^6*g2^4*g3^4) + 2*g1^3*g2*g3^3*t^5.07 + g1^3*g3^2*t^5.13 + g1^3*g2*g3^2*t^5.16 + 4*g1^3*g2^2*g3^2*t^5.18 + (3*t^5.23)/(g1^3*g2^2*g3) + 2*g1^3*g2*g3*t^5.24 + g1^3*g2^2*g3*t^5.27 + t^5.29/(g1^3*g2^3*g3^2) + g1^3*g2^3*g3*t^5.29 + t^5.32/(g1^3*g2^2*g3^2) + (2*t^5.34)/(g1^3*g2*g3^2) + 3*g3^2*t^5.83 + (g3*t^5.89)/g2 + g1^6*g2^2*g3^3*t^5.9 + g3*t^5.91 + g2*g3*t^5.94 + t^5.95/g2^2 - 3*t^6. + g1^6*g2^3*g3^2*t^6.01 + g2^2*t^6.05 - t^6.09/g3 - (g2*t^6.11)/g3 + g1^9*g2^3*g3^6*t^6.47 + 2*g1^3*g2*g3^3*t^6.57 + g1^9*g2^4*g3^5*t^6.58 + t^6.62/(g1^3*g2^3) + g1^3*g2^3*g3^3*t^6.62 + 3*g1^3*g3^2*t^6.63 + g1^3*g2*g3^2*t^6.66 + 4*g1^3*g2^2*g3^2*t^6.68 + g1^9*g2^5*g3^4*t^6.69 + g1^3*g3*t^6.72 + (2*t^6.73)/(g1^3*g2^2*g3) + 6*g1^3*g2*g3*t^6.74 - (2*t^6.76)/(g1^3*g2*g3) + (3*t^6.79)/(g1^3*g2^3*g3^2) + 2*g1^3*g2^3*g3*t^6.79 + g1^3*t^6.8 + g1^9*g2^6*g3^3*t^6.8 - t^6.82/(g1^3*g2^2*g3^2) + (2*t^6.84)/(g1^3*g2*g3^2) + 3*g1^3*g2^2*t^6.85 + (3*t^6.9)/(g1^3*g2^2*g3^3) + t^6.95/(g1^9*g2^6*g3^6) + t^6.95/(g1^3*g3^3) + 2*g1^6*g2^2*g3^5*t^7.23 + g1^6*g2*g3^4*t^7.29 + g1^6*g2^2*g3^4*t^7.32 + 4*g3^2*t^7.33 + 4*g1^6*g2^3*g3^4*t^7.34 + (8*g3*t^7.39)/g2 + 2*g1^6*g2^2*g3^3*t^7.4 + 2*g3*t^7.41 + g1^6*g2^3*g3^3*t^7.43 + 5*g2*g3*t^7.44 + (3*t^7.45)/g2^2 + 4*g1^6*g2^4*g3^3*t^7.45 + (2*t^7.48)/g2 + g1^6*g2^2*g3^2*t^7.49 + 11*t^7.5 + 2*g1^6*g2^3*g3^2*t^7.51 + g2*t^7.52 + g1^6*g2^4*g3^2*t^7.54 + 2*g2^2*t^7.55 + (3*t^7.55)/(g1^6*g2^4*g3^3) + (3*t^7.56)/(g2*g3) + g1^6*g2^5*g3^2*t^7.56 + t^7.59/g3 + t^7.61/(g1^6*g2^5*g3^4) + (3*g2*t^7.61)/g3 + t^7.64/(g1^6*g2^4*g3^4) + (2*t^7.66)/(g1^6*g2^3*g3^4) + 3*g1^3*g2*g3^4*t^7.99 + g1^3*g3^3*t^8.05 + g1^9*g2^3*g3^5*t^8.06 + g1^3*g2*g3^3*t^8.07 + 4*g1^3*g2^2*g3^3*t^8.1 + (g1^3*g3^2*t^8.11)/g2 - t^8.12/(g1^3*g2^3) - g1^3*g2^3*g3^3*t^8.12 + (3*t^8.15)/(g1^3*g2^2) - g1^3*g2*g3^2*t^8.16 + g1^9*g2^4*g3^4*t^8.17 + g1^3*g2^3*g3^2*t^8.21 + 2*g1^3*g3*t^8.22 - g1^3*g2*g3*t^8.24 + t^8.27/(g1^3*g2^4*g3^2) - 5*g1^3*g2^2*g3*t^8.27 + g1^9*g2^5*g3^3*t^8.28 - g1^3*t^8.3 - (6*t^8.32)/(g1^3*g2^2*g3^2) + g1^3*g2^4*g3*t^8.32 - t^8.34/(g1^3*g2*g3^2) - g1^3*g2^2*t^8.35 - g1^3*g2^3*t^8.38 - t^8.4/(g1^3*g2^2*g3^3) - (3*t^8.43)/(g1^3*g2*g3^3) - t^8.45/(g1^3*g3^3) + g1^12*g2^4*g3^8*t^8.63 + 2*g1^6*g2^2*g3^5*t^8.73 + 4*g3^3*t^8.74 + g1^12*g2^5*g3^7*t^8.74 + (g3^2*t^8.78)/g2^2 + g1^6*g2^4*g3^5*t^8.78 + 3*g1^6*g2*g3^4*t^8.79 + (g3^2*t^8.8)/g2 + g1^6*g2^2*g3^4*t^8.82 + 4*g3^2*t^8.83 + 4*g1^6*g2^3*g3^4*t^8.84 + g2*g3^2*t^8.85 + g1^12*g2^6*g3^6*t^8.85 + (g3*t^8.86)/g2^2 + g1^6*g2*g3^3*t^8.88 + (4*g3*t^8.89)/g2 + g1^6*g2^5*g3^4*t^8.89 + 6*g1^6*g2^2*g3^3*t^8.9 - 12*g3*t^8.91 + t^8.93/g2^3 + g1^6*g2^3*g3^3*t^8.93 + t^8.94/(g1^6*g2^5*g3^2) + 2*g2*g3*t^8.94 + (6*t^8.95)/g2^2 + 4*g1^6*g2^4*g3^3*t^8.95 + g2^2*g3*t^8.96 + g1^6*g2*g3^2*t^8.96 + g1^12*g2^7*g3^5*t^8.96 - (7*t^8.98)/g2 + 2*g1^6*g2^2*g3^2*t^8.99 - t^4.5/y - t^6./y - (g1^3*g2*g3^2*t^6.66)/y - (g1^3*g2^2*g3*t^6.77)/y - t^6.82/(g1^3*g2^2*g3^2*y) - (g3*t^7.41)/y + (g1^6*g2^3*g3^3*t^7.43)/y + t^7.48/(g2*y) + t^7.5/y + (2*t^7.59)/(g3*y) + (2*g1^3*g2*g3^3*t^8.07)/y + (g1^3*g3^2*t^8.13)/y + (4*g1^3*g2^2*g3^2*t^8.18)/y + (3*t^8.23)/(g1^3*g2^2*g3*y) + (g1^3*g2*g3*t^8.24)/y + t^8.29/(g1^3*g2^3*g3^2*y) + (g1^3*g2^3*g3*t^8.29)/y + (2*t^8.34)/(g1^3*g2*g3^2*y) - (g1^6*g2^2*g3^4*t^8.82)/y + (g3^2*t^8.83)/y + (2*g3*t^8.89)/(g2*y) + (g1^6*g2^2*g3^3*t^8.9)/y - (g3*t^8.91)/y - (g1^6*g2^3*g3^3*t^8.93)/y + (2*g2*g3*t^8.94)/y - (2*t^8.98)/(g2*y) - t^4.5*y - t^6.*y - g1^3*g2*g3^2*t^6.66*y - g1^3*g2^2*g3*t^6.77*y - (t^6.82*y)/(g1^3*g2^2*g3^2) - g3*t^7.41*y + g1^6*g2^3*g3^3*t^7.43*y + (t^7.48*y)/g2 + t^7.5*y + (2*t^7.59*y)/g3 + 2*g1^3*g2*g3^3*t^8.07*y + g1^3*g3^2*t^8.13*y + 4*g1^3*g2^2*g3^2*t^8.18*y + (3*t^8.23*y)/(g1^3*g2^2*g3) + g1^3*g2*g3*t^8.24*y + (t^8.29*y)/(g1^3*g2^3*g3^2) + g1^3*g2^3*g3*t^8.29*y + (2*t^8.34*y)/(g1^3*g2*g3^2) - g1^6*g2^2*g3^4*t^8.82*y + g3^2*t^8.83*y + (2*g3*t^8.89*y)/g2 + g1^6*g2^2*g3^3*t^8.9*y - g3*t^8.91*y - g1^6*g2^3*g3^3*t^8.93*y + 2*g2*g3*t^8.94*y - (2*t^8.98*y)/g2

Deformation

Here is the data for the deformed fixed points from the chosen fixed point.

#	Superpotential	Central Charge $a$	Central Charge $c$	Ratio $a/c$	$R$-charges	Superconformal Index	More Info.	Rational

Equivalent Fixed Points from Other Seed Theories

Here is a list of equivalent fixed points from other gauge theories.

#	Theory	Superpotential	Central Charge $a$	Central Charge $c$	Ratio $a/c$	$R$-charges	Superconformal Index	More Info.	Rational

Equivalent Fixed Points from the Same Seed Theory

Below is a list of equivalent fixed points from the same seed theories.

id	Theory	Superpotential	Central Charge $a$	Central Charge $c$	Ratio $a/c$	$R$-charges	More Info.	Rational

Previous Theory

The previous fixed point before deforming to get the chosen fixed point.

#	Theory	Superpotential	Central Charge $a$	Central Charge $c$	Ratio $a/c$	$R$-charges	Superconformal Index	More Info.	Rational
58811	SU3adj1nf2	${}\phi_{1}^{4}$ + ${ }q_{1}\tilde{q}_{1}X_{1}$ + ${ }q_{2}\tilde{q}_{1}X_{2}$ + ${ }q_{1}\tilde{q}_{2}X_{3}$ + ${ }q_{2}\tilde{q}_{2}X_{4}$ + ${ }M_{1}\phi_{1}q_{2}\tilde{q}_{2}$ + ${ }M_{2}\phi_{1}q_{1}^{2}q_{2}$ + ${ }M_{3}\phi_{1}\tilde{q}_{1}^{2}\tilde{q}_{2}$	1.0055	1.2242	0.8213	[X:[1.5226, 1.5, 1.5, 1.4774], M:[0.9774, 0.7613, 0.7613], q:[0.2387, 0.2613], qb:[0.2387, 0.2613], phi:[0.5]]	2*t^2.28 + 2*t^2.93 + 3*t^3. + 2*t^3.78 + 2*t^4.43 + 5*t^4.5 + 5*t^4.57 + 6*t^5.22 + 8*t^5.28 + 3*t^5.86 + 3*t^5.93 - t^6. - t^4.5/y - t^6./y - t^4.5*y - t^6.*y	detail