Why AD834+AD811 voltage controlled amplifier does not accept around ground signals?
The AD534 produces a bias current in/out of all its inputs of 45\$\mu A\$ and this current will want to flow into a dc path. Typically, if there was a 1k ohm resistor from Y1 to ground, the offset current would create an input offset voltage of 45mV but, because you don't have a resistor to remove this current on your circuit, the offset voltage rises positively or negatively to some unholy value and your circuit refuses to work.

I think the AD534 is best driven from a device like an op-amp with a low output impedance (this of course is likely given your project). Maybe you can "trim" this offset out at the op-amp stage before the AD534?